L. Diening, P. Hästö, A. Nekvinda, Open problems in variable exponent Lebesgue and Sobolev spaces, in: P. Drábek, J. Rákosník (Eds.), FSDONA04 Proceedings, Milovy, Czech Republic, 2004, pp. 38–58.
Samko, 2005, On a progress in the theory of Lebesgue spaces with variable exponent: Maximal and singular operators, Integral Transforms Spec. Funct., 16, 461, 10.1080/10652460412331320322
L. Diening, P. Harjulehto, P. Hästö, M. Růžička, Lebesgue and Sobolev spaces with variable exponents, Book manuscript, 2010.
Mingione, 2006, Regularity of minima: An invitation to the dark side of the Calculus of Variations, Appl. Math., 51, 10.1007/s10778-006-0110-3
X.-L., 2003, p(x)-Laplacian equations, 117
Orlicz, 1931, Über konjugierte exponentenfolgen, Studia Math., 3, 200, 10.4064/sm-3-1-200-211
Nakano, 1950
Nakano, 1951
Musielak, 1983
Zhikov, 1987, Averaging of functionals of the calculus of variations and elasticity theory, Math. USSR Izv., 29, 33, 10.1070/IM1987v029n01ABEH000958
Kováčik, 1988, Some properties of the spaces Lp(t)(Ω), 98
Kováčik, 1995, Parabolic equations in generalized Sobolev spaces Wk,p(x), Fasc. Math., 25, 87
Fan, 1996, The regularity of Lagrangians f(x,ξ)=|ξ|α(x) with Hölder exponents α(x), Acta Math. Sinica (N.S.), 12, 254, 10.1007/BF02106979
Fan, 1996, Regularity of nonstandard Lagrangians f(x,ξ), Nonlinear Anal., 27, 669, 10.1016/0362-546X(95)00069-8
Fan, 1996, Regularity of minimizers of variational integrals with continuous p(x)-growth conditions, Chinese J. Contemp. Math., 17, 327
Alkhutov, 1997, The Harnack inequality and the Hölder property of solutions of nonlinear elliptic equations with nonstandard growth condition, Differ. Uravn., 33, 1651
Marcellini, 1991, Regularity and existence of solutions of elliptic equations with p,q-growth conditions, J. Differential Equations, 90, 1, 10.1016/0022-0396(91)90158-6
Růžička, 1999, Flow of shear dependent electrorheological fluids: Unsteady space periodic case, 485
Růžička, 2000
Acerbi, 2002, Regularity results for stationary electro-rheological fluids, Arch. Ration. Mech. Anal., 164, 213, 10.1007/s00205-002-0208-7
Acerbi, 2004, Regularity results for parabolic systems related to a class of non-Newtonian fluids, Ann. Inst. H. Poincaré Anal. Non Linéaire, 21, 25, 10.1016/j.anihpc.2002.11.002
Antontsev, 2006, On stationary thermo-rheological viscous flows, Ann. Univ. Ferrara Sez. VII Sci. Mat., 52, 19, 10.1007/s11565-006-0002-9
Chen, 2006, Variable exponent, linear growth functionals in image restoration, SIAM J. Appl. Math., 66, 1383, 10.1137/050624522
Aboulaich, 2008, New diffusion models in image processing, Comput. Math. Appl., 56, 874, 10.1016/j.camwa.2008.01.017
Bollt, 2009, Graduated adaptive image denoising: Local compromise between total variation and isotropic diffusion, Adv. Comput. Math., 31, 61, 10.1007/s10444-008-9082-7
A. El Hamidi, C. Ghannam, G. Bailly-Maitre, M. Menard, Nonstandard diffusion in image restoration and decomposition, Preprint, 2009.
Levine, 2005, An adaptive variational model for image decomposition, vol. 3757, 382, 10.1007/11585978_25
Eleuteri, 2008, Regularity results for a class of obstacle problems under nonstandard growth conditions, J. Math. Anal. Appl., 344, 1120, 10.1016/j.jmaa.2008.03.068
M. Eleuteri, J. Habermann, A Hölder continuity result for a class of obstacle problems under non standard growth conditions, Math. Nachr. (in press).
M. Eleuteri, J. Habermann, Calderón–Zygmund type estimates for a class of obstacle problems with p(x) growth, Preprint, 2010.
Harjulehto, 2007, An obstacle problems and superharmonic functions with nonstandard growth, Nonlinear Anal., 67, 3424, 10.1016/j.na.2006.10.026
Rodrigues, 2008, The obstacle problem for nonlinear elliptic equations with variable growth and L1-data, Monatsh. Math., 154, 303, 10.1007/s00605-008-0550-4
Antontsev, 2005, A model porous medium equation with variable exponent of nonlinearity: Existence, uniqueness and localization properties of solutions, Nonlinear Anal., 60, 515, 10.1016/S0362-546X(04)00393-1
Henriques, 2006, Intrinsic scaling for PDE’s with an exponential nonlinearity, Indiana Univ. Math. J., 55, 1701, 10.1512/iumj.2006.55.2715
Dai, 2009, Existence of solutions for a p(x)-Kirchhoff-type equation, J. Math. Anal. Appl., 359, 275, 10.1016/j.jmaa.2009.05.031
Dai, 2009, Infinitely many positive solutions for a p(x)-Kirchhoff-type equation, J. Math. Anal. Appl., 359, 704, 10.1016/j.jmaa.2009.06.012
Autuori, 2009, Asymptotic stability for anisotropic Kirchhoff systems, J. Math. Anal. Appl., 352, 149, 10.1016/j.jmaa.2008.04.066
G. Autuori, P. Pucci, M.C. Salvatori, Global nonexistence for nonlinear Kirchhoff systems, Arch. Ration. Mech. Anal. (in press).
Diening, 2003, Calderón–Zygmund operators on generalized Lebesgue spaces Lp(⋅) and problems related to fluid dynamics, J. Reine Angew. Math., 563, 197, 10.1515/crll.2003.081
Pinasco, 2009, Blow-up for parabolic and hyperbolic problems with variable exponents, Nonlinear Anal., 71, 1094, 10.1016/j.na.2008.11.030
Calotă, 2008, On some quasilinear elliptic equations with critical Sobolev exponents and non-standard growth conditions, Bull. Belg. Math. Soc. Simon Stevin, 15, 249, 10.36045/bbms/1210254822
Garcia Melian, 2009, Existence, asymptotic behavior and uniqueness for large solutions to Δu=eq(x)u, Adv. Nonlinear Stud., 9, 395, 10.1515/ans-2009-0208
Garcia Melian, 2009, Large solutions for the Laplacian with a power nonlinearity given by a variable exponent, Ann. Inst. H. Poincaré Anal. Non Linéaire, 26, 889, 10.1016/j.anihpc.2008.03.007
Zhang, 2007, Existence and asymptotic behavior of blow-up solutions to a class of p(x)-Laplacian problems, J. Math. Anal. Appl., 329, 472, 10.1016/j.jmaa.2006.06.089
Zhang, 2008, Boundary blow-up solutions to p(x)-Laplacian equations with exponential nonlinearities, J. Inequal. Appl., 10.1155/2008/279306
Zhang, 2009, On the boundary blow-up solutions of p(x)-Laplacian equations with singular coefficient, Nonlinear Anal., 70, 4053, 10.1016/j.na.2008.08.014
Habermann, 2008, Partial regularity for minima of higher order functionals with p(x)-growth, Manuscripta Math., 126, 1, 10.1007/s00229-007-0147-6
Habermann, 2008, Calderón–Zygmund estimates for higher order systems with p(x) growth, Math. Z., 258, 427, 10.1007/s00209-007-0180-x
Cianci, 2009, Boundedness of solutions for an elliptic equation with non-standard growth, Nonlinear Anal., 71, 1825, 10.1016/j.na.2009.01.017
T. Adamowicz, P. Hästö, Mappings of finite distortion and PDE with nonstandard growth, Int. Math. Res. Not. IMRN (2010), in press (doi:10.1093/imrn/rnp192).
Bonder, 2010, A free boundary problem for the p(x)-Laplacian, Nonlinear Anal., 72, 1078, 10.1016/j.na.2009.07.048
Harjulehto, 2007, Variable exponent Sobolev spaces with zero boundary values, Math. Bohem., 132, 125, 10.21136/MB.2007.134186
Heinonen, 1993
Kinderlehrer, 1980, vol. 88
Malý, 1997, vol. 51
Harjulehto, 2003, The Dirichlet energy integral on intervals in variable exponent Sobolev spaces, Z. Anal. Anwend., 22, 911, 10.4171/ZAA/1179
Fan, 2003, A Knobloch-type result for p(t)-Laplacian systems, J. Math. Anal. Appl., 282, 453, 10.1016/S0022-247X(02)00376-1
Wang, 2009, Existence of periodic solutions for p(t)-Laplacian systems, Nonlinear Anal., 70, 866, 10.1016/j.na.2008.01.017
Fan, 2003, Hartman-type results for p(t)-Laplacian systems, Nonlinear Anal., 52, 585, 10.1016/S0362-546X(02)00124-4
Zhang, 2007, Oscillatory property of solutions for p(t)-Laplacian equations, J. Inequal. Appl., 10.1155/2007/58548
Zhang, 2009, Existence of multiple solutions for weighted p(r)-Laplacian equation Dirichlet problems, Nonlinear Anal., 70, 3721, 10.1016/j.na.2008.07.028
Zhang, 2009, Existence of solutions and nonnegative solutions for weighted p(r)-Laplacian impulsive system multi-point boundary value problems, Nonlinear Anal., 71, 3814, 10.1016/j.na.2009.02.040
Zhang, 2009, Existence of solutions for weighted p(r)-Laplacian impulsive system periodic-like boundary value problems, Nonlinear Anal., 71, 3596, 10.1016/j.na.2009.02.043
Hästö, 2006, On the variable exponent Dirichlet energy integral, Commun. Pure Appl. Anal., 5, 413, 10.3934/cpaa.2006.5.415
Harjulehto, 2006, The Dirichlet energy integral and variable exponent Sobolev spaces with zero boundary values, Potential Anal., 25, 205, 10.1007/s11118-006-9023-3
Harjulehto, 2008, Minimizers of the variable exponent, non-uniformly convex Dirichlet energy, J. Math. Pures Appl. (9), 89, 174, 10.1016/j.matpur.2007.10.006
Harjulehto, 2009, Harnack’s inequality for p(⋅)-harmonic functions with unbounded exponent p, J. Math. Anal. Appl., 352, 345, 10.1016/j.jmaa.2008.05.090
Manfredi, 2009, p(x)-harmonic function with unbounded exponent in a subdomain, Ann. Inst. H. Poincaré Anal. Non Linéaire, 26, 2581, 10.1016/j.anihpc.2009.09.008
P. Lindqvist, T. Lukkari, A curious equation involving the infinity-Laplacian, Adv. Calc. Var. 2009 (in press).
Manfredi, 2010, Limits as p(x)→∞ of p(x)-harmonic functions, Nonlinear Anal., 72, 309, 10.1016/j.na.2009.06.054
Perez-Llanos, 2010, The behaviour of the p(x)-Laplacian eigenvalue problem as p(x)→infinity, J. Math. Anal. Appl., 363, 502, 10.1016/j.jmaa.2009.09.044
Coscia, 2002, Integral representation and Γ-convergence of variational integrals with p(x)-growth, ESAIM Control Optim. Calc. Var., 7, 495, 10.1051/cocv:2002065
Galewska, 2006, On the stability of solutions for the p(x)-Laplacian equation and some applications to optimisation problems with state constraints, ANZIAM J., 48, 245, 10.1017/S1446181100003072
Fan, 2005, Eigenvalues of p(x)-Laplacian Dirichlet problem, J. Math. Anal. Appl., 302, 306, 10.1016/j.jmaa.2003.11.020
Allegretto, 2007, Form estimates for the p(x)-Laplacian, Proc. Amer. Math. Soc., 135, 2177, 10.1090/S0002-9939-07-08718-7
Fan, 2008, A constrained minimization problem involving the p(x)-Laplacian in image, Nonlinear Anal., 69, 3661, 10.1016/j.na.2007.10.002
Fan, 2007, Eigenvalues of the p(x)-Laplacian Neumann problem, Nonlinear Anal., 67, 2982, 10.1016/j.na.2006.09.052
Deng, 2008, Eigenvalues of the p(x)-Laplacian Steklov problem, J. Math. Anal. Appl., 339, 925, 10.1016/j.jmaa.2007.07.028
Deng, 2009, A local mountain pass theorem and applications to a double perturbed p(x)-Laplacian equations, Appl. Math. Comput., 211, 234, 10.1016/j.amc.2009.01.042
Mihăilescu, 2007, On a nonhomogeneous quasilinear eigenvalue problem in Sobolev spaces with variable exponent, Proc. Amer. Math. Soc., 135, 2929, 10.1090/S0002-9939-07-08815-6
Mihăilescu, 2008, Eigenvalue problems for anisotropic quasilinear elliptic equations with variable exponent, J. Math. Anal. Appl., 340, 687, 10.1016/j.jmaa.2007.09.015
Kurata, 2008, Compact embedding from W01,2(Ω) to Lq(x)(Ω) and its application to nonlinear elliptic boundary value problem with variable critical exponent, J. Math. Anal. Appl., 339, 1386, 10.1016/j.jmaa.2007.07.083
Fan, 2009, Remarks on eigenvalue problems involving the p(x)-Laplacian, J. Math. Anal. Appl., 352, 85, 10.1016/j.jmaa.2008.05.086
Zhang, 2007, Existence and asymptotic behavior of positive solutions to p(x)-Laplacian equations with singular nonlinearities, J. Inequal. Appl., 10.1155/2007/19349
Fan, 2003, Existence of solutions for p(x)-Laplacian Dirichlet problem, Nonlinear Anal., 52, 1843, 10.1016/S0362-546X(02)00150-5
Sanchón, 2009, Entropy solutions for the p(x)-Laplace equation, Trans. Amer. Math. Soc., 361, 6387, 10.1090/S0002-9947-09-04399-2
Iliaş, 2007, Existence and multiplicity of solutions of a p(x)-Laplacian equation in a bounded domain, Rev. Roumaine Math. Pures Appl., 52, 639
Chabrowski, 2005, Existence of solutions for p(x)-Laplacian problems on a bounded domain, J. Math. Anal. Appl., 306, 604, 10.1016/j.jmaa.2004.10.028
Antontsev, 2006, Elliptic equations and systems with nonstandard growth conditions: Existence, uniqueness and localization properties of solutions, Nonlinear Anal., 65, 728, 10.1016/j.na.2005.09.035
Antontsev, 2007, Parabolic equations with anisotropic nonstandard growth conditions, vol. 154, 33
Antontsev, 2009, Elliptic boundary value problems with nonstandard growth conditions, Nonlinear Anal., 71, 891, 10.1016/j.na.2008.10.109
Dai, 2009, Infinitely many solutions for a hemivariational inequality involving the p(x)-Laplacian, Nonlinear Anal., 71(, 186, 10.1016/j.na.2008.10.039
Dai, 2009, Infinitely many solutions for a p(x)-Laplacian equation in RN, Nonlinear Anal., 71, 1133, 10.1016/j.na.2008.11.037
Dai, 2009, Infinitely many non-negative solutions for a Dirichlet problem involving p(x)-Laplacian, Nonlinear Anal., 71, 5840, 10.1016/j.na.2009.05.007
Fan, 2008, p(x)-Laplacian equations in Rn with periodic data and nonperiodic perturbations, J. Math. Anal. Appl., 341, 103, 10.1016/j.jmaa.2007.10.006
Fan, 2007, Remarks on Ricceri’s variational principle and applications to the p(x)-Laplacian equations, Nonlinear Anal., 67, 3064, 10.1016/j.na.2006.09.060
Fan, 2009, Multiplicity of positive solutions for a class of inhomogeneous Neumann problems involving the p(x)-Laplacian, NoDEA Nonlinear Differential Equations Appl., 16, 255, 10.1007/s00030-008-6027-2
Fan, 2004, Existence and multiplicity of solutions for p(x)-Laplacian equations in RN, Nonlinear Anal., 59, 173, 10.1016/S0362-546X(04)00254-8
Fan, 2006, Regularity of quasi-minimizers of integral functionals with discontinuous p(x)-growth conditions, Nonlinear Anal., 65, 1521, 10.1016/j.na.2005.10.027
Fan, 2007, Nodal solutions of p(x)-Laplacian equations, Nonlinear Anal., 67, 2859, 10.1016/j.na.2006.09.045
Fu, 2009, The principle of concentration compactness in Lp(x) spaces and its application, Nonlinear Anal., 71, 1876, 10.1016/j.na.2009.01.023
Fu, 2009, A multiplicity result for p(x)-Laplacian problem in RN, Nonlinear Anal., 70, 2261, 10.1016/j.na.2008.03.038
Iliaş, 2008, Dirichlet problem with p(x)-Laplacian, Math. Rep. (Bucur.), 10, 43
Liu, 2008, Existence of positive solutions for p(x)-Laplacian equations in unbounded domains, Nonlinear Anal., 69, 3358, 10.1016/j.na.2007.09.027
Mihăilescu, 2006, Elliptic problems in variable exponent spaces, Bull. Austral. Math. Soc., 74, 197, 10.1017/S0004972700035644
Yao, 2008, Solutions for Neumann boundary value problems involving p(x)-Laplace operators, Nonlinear Anal., 68, 1271, 10.1016/j.na.2006.12.020
Zhang, 2008, Existence of solutions for p(x)-Laplacian equations with singular coefficients in RN, J. Math. Anal. Appl., 348, 38, 10.1016/j.jmaa.2008.06.026
Zang, 2008, p(x)-Laplacian equations satisfying Cerami condition, J. Math. Anal. Appl., 337, 547, 10.1016/j.jmaa.2007.04.007
Ben Ali, 2008, On a nonhomogeneous quasilinear problem in Sobolev spaces with variable exponent, Bul. Ştiinţ. Univ. Piteşti Ser. Mat. Inf., 14, 19
Boureanu, 2006, Existence of solutions for an elliptic equation involving the p(x)-Laplace operator, Electron. J. Differential Equations, 97, 1
Mihăilescu, 2007, Existence and multiplicity of solutions for a Neumann problem involving the p(x)-Laplace operator, Nonlinear Anal., 67, 1419, 10.1016/j.na.2006.07.027
Yao, 2008, On an open problem involving the p(x)-Laplacian—A further study on the multiplicity of weak solutions to p(x)-Laplacian equations, Nonlinear Anal., 69, 1445, 10.1016/j.na.2007.06.044
Papageorgiou, 2008, A multiplicity theorem for a variable exponent Dirichlet problem, Glasg. Math. J., 50, 335, 10.1017/S0017089508004242
Mihăilescu, 2006, Existence and multiplicity of solutions for an elliptic equation with p(x)-growth conditions, Glasg. Math. J., 48, 411, 10.1017/S0017089506003144
Liu, 2008, Existence of three solutions for p(x)-Laplacian equations, Nonlinear Anal., 68, 2119, 10.1016/j.na.2007.01.035
Ji, 2008, Perturbation for a p(x)-Laplacian equation involving oscillating nonlinearities in RN, Nonlinear Anal., 69, 2393, 10.1016/j.na.2007.08.018
Galewski, 2007, On the existence and stability of solutions for Dirichlet problem with p(x)-Laplacian, J. Math. Anal. Appl., 326, 352, 10.1016/j.jmaa.2006.03.006
Galewski, 2007, On a Dirichlet problem with generalized p(x)-Laplacian and some applications, Numer. Funct. Anal. Optim., 28, 1087, 10.1080/01630560701404948
Galewski, 2008, On a Dirichlet problem with p(x)-Laplacian, J. Math. Anal. Appl., 337, 281, 10.1016/j.jmaa.2007.03.096
Alves, 2008, Existence of solution for a degenerate p(x)-Laplacian equation in RN, J. Math. Anal. Appl., 345, 731, 10.1016/j.jmaa.2008.04.060
Corrêa, 2007, On a singular elliptic problem involving the p(x)-Laplacian and generalized Lebesgue–Sobolev spaces, Adv. Math. Sci. Appl., 17, 639
Lukkari, 2008, Elliptic equations with nonstandard growth involving measures, Hiroshima Math. J., 38, 155, 10.32917/hmj/1207580349
Mihăilescu, 2008, On a class of nonlinear problems involving a p(x)-Laplace type operator, Czechoslovak Math. J., 58, 155, 10.1007/s10587-008-0011-1
Mihăilescu, 2006, A multiplicity result for a nonlinear degenerate problem arising in the theory of electrorheological fluids, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 462, 2625, 10.1098/rspa.2005.1633
Mihăilescu, 2008, Continuous spectrum for a class of nonhomogeneous differential operators, Manuscripta Math., 125, 157, 10.1007/s00229-007-0137-8
Mihăilescu, 2010, On a non-homogeneous eigenvalue problem involving a potential: An Orlicz–Sobolev space setting, J. Math. Pures Appl., 93, 132, 10.1016/j.matpur.2009.06.004
Dinu, 2006, Nonlinear eigenvalue problems in Sobolev spaces with variable exponent, J. Funct. Spaces Appl., 4, 225, 10.1155/2006/515496
Boureanu, 2008, Existence and multiplicity of solutions for a Neumann problem involving variable exponent growth conditions, Glasg. Math. J., 50, 565, 10.1017/S0017089508004424
Rovenţa, 2008, Boundary asymptotic and uniqueness of solution for a problem with p(x)-Laplacian, J. Inequal. Appl., 10.1155/2008/609047
Fu, 2002, The existence of solutions for elliptic systems with nonuniform growth, Studia Math., 151, 227, 10.4064/sm151-3-3
Diening, 2005, Strong solutions for generalized Newtonian fluids, J. Math. Fluid Mech., 7, 413, 10.1007/s00021-004-0124-8
Zhang, 2007, Existence of positive solutions for elliptic systems with nonstandard p(x)-growth conditions via sub–supersolution method, Nonlinear Anal., 67, 1055, 10.1016/j.na.2006.06.017
Zhang, 2007, Existence of positive solutions for a class of p(x)-Laplacian systems, J. Math. Anal. Appl., 333, 591, 10.1016/j.jmaa.2006.11.037
Zhang, 2009, Existence and asymptotic behavior of positive solutions for variable exponent elliptic systems, Nonlinear Anal., 70, 305, 10.1016/j.na.2007.12.001
Afrouzi, 2007, Existence of positive solutions for p(x)-Laplacian problems, Electron. J. Differential Equations, 177, 1
El Hamidi, 2004, Existence results to elliptic systems with nonstandard growth conditions, J. Math. Anal. Appl., 300, 30, 10.1016/j.jmaa.2004.05.041
Xu, 2008, Existence and multiplicity of solutions for elliptic systems with nonstandard growth condition in RN, Nonlinear Anal., 68, 956, 10.1016/j.na.2006.11.052
Ogras, 2008, Existence of solutions for a class of elliptic systems in RN involving the (p(x),q(x))-Laplacian, J. Inequal. Appl., 10.1155/2008/612938
Liu, 2009, Existence of three solutions for a class of quasilinear elliptic systems involving the (p(x),q(x))-Laplacian, Nonlinear Anal., 71, 550, 10.1016/j.na.2008.10.094
Guo, 2009, Infinitely many periodic solutions for variable exponent systems, J. Inequal. Appl., 10.1155/2009/714179
Harjulehto, 2007, Unbounded supersolutions of nonlinear equations with nonstandard growth, Bound. Value Probl., 10.1155/2007/48348
Alkhutov, 2004, Continuity at boundary points of solutions of quasilinear elliptic equations with a non-standard growth condition, Izv. Ross. Akad. Nauk Ser. Mat., 68, 3
P. Harjulehto, P. Hästö, V. Latvala, Boundedness of solutions of the non-uniformly convex, non-standard growth Laplacian, Preprint, 2010.
Fan, 2003, A strong maximum principle for p(x)-Laplace equations, Chinese J. Contemp. Math., 24, 277
Fortini, 2009, Maximum principles for anisotropic elliptic inequalities, Nonlinear Anal., 70, 2917, 10.1016/j.na.2008.12.030
Hästö, 2005, Counter-examples of regularity in variable exponent Sobolev spaces, vol. 367
Zhikov, 1995, On Lavrentiev’s phenomenon, Russ. J. Math. Phys., 3, 249
M. Eleuteri, P. Harjulehto, T. Lukkari, Global regularity and stability of solutions to elliptic equations with nonstandard growth, Complex Var. Elliptic Equ. (in press).
Alkhutov, 2005, On the Hölder continuity of p(x)-harmonic functions, Mat. Sb., 196, 3
Harjulehto, 2008, Fine topology of variable exponent energy superminimizers, Ann. Acad. Sci. Fenn. Math., 33, 491
T. Lukkari, F.-Y. Maeda, N. Marola, Wolff potential estimates for elliptic equations with nonstandard growth and applications. Forum Math. (in press).
Lukkari, 2009, Singular solutions of elliptic equations with nonstandard growth, Math. Nachr., 282, 1770, 10.1002/mana.200610822
V. Latvala, T. Lukkari, O. Toivanen, The fundamental convergence theorem for p(⋅)-superharmonic functions, Preprint, 2009.
Pastukhova, 2008, Improved integrability of the gradients of solutions of elliptic equations with variable nonlinearity exponent, Sb. Math., 199, 1751, 10.1070/SM2008v199n12ABEH003980
Fan, 1999, A class of De Giorgi type and Hölder continuity, Nonlinear Anal., 36, 295, 10.1016/S0362-546X(97)00628-7
Fan, 2000, The quasi-minimizer of integral functionals with m(x) growth conditions, Nonlinear Anal., 39, 807, 10.1016/S0362-546X(98)00239-9
Acerbi, 2001, Regularity results for a class of functionals with non-standard growth, Arch. Ration. Mech. Anal., 156, 121, 10.1007/s002050100117
Coscia, 1999, Hölder continuity of the gradient of p(x)-harmonic mappings, C. R. Acad. Sci. Paris, 328, 363, 10.1016/S0764-4442(99)80226-2
Giaquinta, 1982, One the regularity of the minima of variational integrals, Acta Math., 148, 31, 10.1007/BF02392725
Giaquinta, 1984, Quasiminima, Ann. Inst. H. Poincaré Anal. Non Linéaire, 1, 79, 10.1016/S0294-1449(16)30429-2
Habermann, 2008, Regularity for minimizers of functionals with nonstandard growth by A-harmonic approximation, NoDEA Nonlinear Differential Equations Appl., 15, 169, 10.1007/s00030-007-7007-7
Eleuteri, 2004, Hölder continuity results for a class of functionals with non standard growth, Boll. Unione Mat. Ital., 7-B, 129
Acerbi, 2001, Regularity results for a class of quasiconvex functionals with nonstandard growth, Ann. Sc. Norm. Super. Pisa Cl. Sci. (4), 30, 311
Acerbi, 2005, Gradient estimates for the p(x)-Laplacian system, J. Reine Angew. Math., 584, 117, 10.1515/crll.2005.2005.584.117
Zhikov, 1997, Meyer-type estimates for solving the nonlinear Stokes system, Differ. Equ., 33, 108
Zhikov, 1997, On some variational problems, Russ. J. Math. Phys., 5, 105
Chiadò Piat, 1997, Hölder continuity of minimizers of functionals with variable growth exponent, Manuscripta Math., 93, 283, 10.1007/BF02677472
Harjulehto, 2008, Harnack’s inequality for quasiminimizers with non-standard growth conditions, J. Math. Anal. Appl., 344, 504, 10.1016/j.jmaa.2008.03.018
Fan, 2007, Global C1,α regularity for variable exponent elliptic equations in divergence form, J. Differential Equations, 235, 397, 10.1016/j.jde.2007.01.008
T. Lukkari, Boundary continuity of solutions to elliptic equations with nonstandard growth, Preprint, 2009.
Li, 2001
Chen, 2006, Hölder continuity of weak solutions for parabolic equations with nonstandard growth conditions, Acta Math. Sin. (Engl. Ser.), 22, 793, 10.1007/s10114-005-0582-9
DiBenedetto, 1993
DiBenedetto, 2008, Harnack estimates for quasi-linear degenerate parabolic differential equations, Acta Math., 200, 181, 10.1007/s11511-008-0026-3
Urbano, 2008, vol. 1930
Antontsev, 2005, Higher integrability for parabolic equations of p(x,t)-Laplacian type, Adv. Differential Equations, 10, 1053, 10.57262/ade/1355867817
M. Nuortio, Local boundedness for parabolic variable exponent PDE, Internationally unpublished Licentiate of Philosophy Thesis, University of Oulu, 2008.
Diening, 2007, C1,α-regularity for electrorheological fluids in two dimensions, NoDEA Nonlinear Differential Equations Appl., 14, 207, 10.1007/s00030-007-5026-z
Crispo, 2009, On the C1,γ(Ω¯)∩W2,2(Ω) regularity for a class of electro-rheological fluids, J. Math. Anal. Appl., 356, 119, 10.1016/j.jmaa.2009.02.013
Bendahmane, 2009, Renormalized solutions for nonlinear elliptic equations with variable exponents and L1 data, Nonlinear Anal., 70, 567, 10.1016/j.na.2007.12.027
Bögelein, 2007, Higher integrability of very weak solutions of systems of p(x)-Laplacian type, J. Math. Anal. Appl., 336, 480, 10.1016/j.jmaa.2007.02.019
Iwaniec, 1994, Weak minima of variational integrals, J. Reine Angew. Math., 454, 143, 10.1515/crll.1994.454.143
Lewis, 1993, On very weak solutions of certain elliptic systems, Comm. Partial Differential Equations, 18, 1515, 10.1080/03605309308820984
Bögelein, 2009, Very weak solutions of higher order degenerate parabolic systems, Adv. Differential Equations, 14, 121
Kinnunen, 2002, Very weak solutions of parabolic systems of p-Laplacian type, Ark. Mat., 40, 105, 10.1007/BF02384505
Bénilan, 1995, An L1-theory of existence and uniqueness of solutions of nonlinear elliptic equations, Ann. Sc. Norm. Super. Pisa Cl. Sci. (4), 22, 241