Partial regularity for symmetric quasiconvex functionals on BD
Tài liệu tham khảo
Acerbi, 1987, A regularity theorem for minimizers of quasiconvex integrals, Arch. Ration. Mech. Anal., 99, 261, 10.1007/BF00284509
Acerbi, 2002, Regularity results for stationary electro-rheological fluids, Arch. Ration. Mech. Anal., 164, 213, 10.1007/s00205-002-0208-7
Ambrosio, 1997, Fine properties of functions with bounded deformation, Arch. Ration. Mech. Anal., 139, 201, 10.1007/s002050050051
Alberti, 1993, Rank one property for derivatives of functions with bounded variation, Proc. R. Soc. Edinb., Sect. A, 123, 239, 10.1017/S030821050002566X
Ambrosio, 1992, On the relaxation in BV(Ω;Rm) of quasi–convex integrals, J. Funct. Anal., 109, 76, 10.1016/0022-1236(92)90012-8
Ambrosio, 2000, Functions of Bounded Variation and Free Discontinuity Problems
Anzellotti, 1980, Existence of the displacements field for an elastoplastic body subject to Hencky's law and Von Mises yield condition, Manuscr. Math., 32, 101, 10.1007/BF01298185
Anzellotti, 1988, Convex functionals and partial regularity, Arch. Ration. Mech. Anal., 102, 243, 10.1007/BF00281349
Arroyo-Rabasa
Babadjian, 2015, Traces of functions of bounded deformation, Indiana Univ. Math. J., 64, 1271, 10.1512/iumj.2015.64.5601
Barroso, 2000, A relaxation theorem in the space of functions of bounded deformation, Ann. Sc. Norm. Super. Pisa, Cl. Sci. (4), 29, 19
Beck, 2016, Elliptic Regularity - A First Course, vol. 19
Bildhauer, 2003, Convex Variational Problems – Linear, Nearly Linear and Anisotropic Growth Conditions, vol. 1818
Bourgain, 2004, H12 maps with values into the circle: minimal connections, lifting, and the Ginzburg-Landau equation, Publ. Math. Inst. Hautes Études Sci., 99, 1, 10.1007/s10240-004-0019-5
Breit, 2012, Sharp conditions for korn inequalities in Orlicz spaces, J. Math. Fluid Mech., 14, 565, 10.1007/s00021-011-0082-x
Breit, 2020, On the trace operator for functions of bounded A-variation, Anal. PDE, 13, 559, 10.2140/apde.2020.13.559
Buckley, 1994, Sobolev-Poincaré inequalities for p<1, Indiana Univ. Math. J., 43, 221, 10.1512/iumj.1994.43.43011
Carozza, 1998, Partial regularity of minimizers of quasiconvex integrals with subquadratic growth, Ann. Mat. Pura Appl. (4), 175, 141, 10.1007/BF01783679
Christiansen, 1979
Ciarlet, 1998, Inequalities of Korn's type on surfaces, vol. 140, 105
Ciarlet, 2006, A nonlinear Korn inequality on a surface, J. Math. Pures Appl., 85, 2, 10.1016/j.matpur.2005.10.010
Ciarlet, 2015, Nonlinear Korn inequalities, J. Math. Pures Appl., 104, 1119, 10.1016/j.matpur.2015.07.007
S. Conti, D. Faraco, F. Maggi, a new approach to counterexamples to L 1 estimates: Korn's inequality, geometric rigidity, and regularity for gradients of separately convex functions, Archive for rational mechanics and analysis 175 (2), 287–300.
Conti, 2019, A note on the Hausdorff dimension of the singular set of solutions to elasticity type systems, Commun. Contemp. Math., 21, 10.1142/S0219199719500263
Dacorogna, 1982, Weak Continuity and Weak Lower Semicontinuity of Nonlinear Func- Tionals, vol. 922
Dal Maso, 2004, Higher order quasiconvexity reduces to quasiconvexity, Arch. Ration. Mech. Anal., 171, 55, 10.1007/s00205-003-0278-1
De Philippis, 2016, On the structure of A—free measures and applications, Ann. Math. (2), 184, 1017, 10.4007/annals.2016.184.3.10
De Philippis, 2017, Characterization of generalized Young measures generated by symmetric gradients, Arch. Ration. Mech. Anal., 224, 1087, 10.1007/s00205-017-1096-1
Diening, 2008, Fractional estimates for non-differentiable elliptic systems with general growth, Forum Math., 523
Diening, 2012, Partial regularity for minimizers of functionals with general growth, SIAM J. Math. Anal., 44, 3594, 10.1137/120870554
Duzaar, 2000, Optimal interior partial regularity for nonlinear elliptic systems: the method of A-harmonic approximation, Manuscr. Math., 103, 267, 10.1007/s002290070007
Duzaar, 2002, Optimal interior and boundary regularity for almost minimizers to elliptic variational integrals, J. Reine Angew. Math., 546, 73
Duzaar, 2005, Regularity of almost minimizers of quasi-convex variational integrals with subquadratic growth, Ann. Mat. Pura Appl. (4), 184, 421, 10.1007/s10231-004-0117-5
Ekeland, 1974, On the variational principle, J. Math. Anal. Appl., 47, 324, 10.1016/0022-247X(74)90025-0
Evans, 1986, Quasiconvexity and partial regularity in the calculus of variations, Arch. Ration. Mech. Anal., 95, 227, 10.1007/BF00251360
Fonseca, 1993, Relaxation of quasiconvex functionals in BV(Ω;Rp) for integrands f(x,u,∇u), Arch. Ration. Mech. Anal., 123, 1, 10.1007/BF00386367
Fonseca, 1999, A-quasiconvexity, lower semicontinuity, and Young measures, SIAM J. Math. Anal., 30, 1355, 10.1137/S0036141098339885
Friedrichs, 1947, On the boundary value problems of the theory of elasticity and Korn's inequality, Ann. Math., 48, 441, 10.2307/1969180
Fuchs, 2000, Variational Methods for Problems from Plasticity Theory and for Generalized Newtonian Fluids, vol. 1749
Giaquinta, 1983, Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems, vol. 105
Giusti, 2003
Gmeineder, 2016, Symmetric-convex functionals of linear growth, J. Elliptic Parabolic Equ., 2, 59, 10.1007/BF03377392
Gmeineder, 2020, The regularity of minima for the Dirichlet problem on BD, Arch. Ration. Mech. Anal., 237, 1099, 10.1007/s00205-020-01507-5
Gmeineder, 2019, Sobolev regularity for convex functionals on BD, J. Calc. Var., 58, 56, 10.1007/s00526-019-1491-6
Gmeineder, 2019, Partial regularity for BV minimizers, Arch. Ration. Mech. Anal., 232, 1429, 10.1007/s00205-018-01346-5
Gmeineder, 2019, On critical Lp-differentiability of BD-maps, Rev. Mat. Iberoam., 35, 2071, 10.4171/rmi/1111
Gobert, 1962, Une inéquation fondamentale de la théorie de l'élasticité, Bull. Soc. R. Sci. Liège, 3–4, 182
Kirchheim, 2016, On rank one convex functions that are homogeneous of degree one, Arch. Ration. Mech. Anal., 221, 527, 10.1007/s00205-016-0967-1
Kohn, 1979
Kohn, 1982, New integral estimates for deformations in terms of their nonlinear strains, Arch. Ration. Mech. Anal., 78, 131, 10.1007/BF00250837
Kolyada, 1993, On the embedding of Sobolev spaces, Mat. Zametki, 54, 48
Kristensen, 2007, The singular set of Lipschitzian minima of multiple integrals, Arch. Ration. Mech. Anal., 184, 341, 10.1007/s00205-006-0036-2
Kristensen, 2010, Relaxation of signed integral functionals in BV, Calc. Var. Partial Differ. Equ., 37, 29, 10.1007/s00526-009-0250-5
Kuusi, 2016, Partial regularity and potentials, J. Éc. Polytech. Math., 3, 309, 10.5802/jep.35
Maz'ya, 2009, Theory of Sobolev Multipliers, vol. 307
Mingione, 2003, The singular set of solutions to non-differentiable elliptic systems, Arch. Ration. Mech. Anal., 166, 287, 10.1007/s00205-002-0231-8
Mingione, 2003, Bounds for the singular set of solutions to non linear elliptic systems, Calc. Var. Partial Differ. Equ., 18, 373, 10.1007/s00526-003-0209-x
Mingione, 2006, Regularity of minima: an invitation to the dark side of the calculus of variations, Appl. Math., 51, 355, 10.1007/s10778-006-0110-3
Morrey, 2008, Multiple integrals in the calculus of variations
Mosolov, 1972, On the correctness of boundary value problems in the mechanics of continuous media, Math. USSR Sb., 17, 257, 10.1070/SM1972v017n02ABEH001503
Nečas, 1966, Sur les normes équivalentes dans Wkp(Ω) et sur la coecivité des formes formellement positives, 102
Ornstein, 1962, A non-equality for differential operators in the L1-norm, Arch. Ration. Mech. Anal., 11, 40, 10.1007/BF00253928
Reshetnyak, 1968, Weak convergence of completely additive vector functions on a set, Sib. Mat. Zh., 9, 1386, 10.1007/BF02196453
Rindler, 2011, Lower semicontinuity for integral functionals in the space of functions of bounded deformation via rigidity and Young measures, Arch. Ration. Mech. Anal., 202, 63, 10.1007/s00205-011-0408-0
Schmidt, 2014, Partial regularity for degenerate variational problems and image restoration models in BV, Indiana Univ. Math. J., 63, 213, 10.1512/iumj.2014.63.5174
Schmidt, 2015
Schmidt, 2009, A simple partial regularity proof for minimizers of variational integrals, Nonlinear Differ. Equ. Appl., 16, 109, 10.1007/s00030-008-8012-1
Strang, 1981, Functions of bounded deformation, Arch. Ration. Mech. Anal., 75, 7
Strauss, 1973, Variations of Korn's and Sobolev's inequalities, vol. XXIII, 207
Suquet, 1979, Un espace fonctionnel pour les équations de la plasticité, Ann. Fac. Sci. Toulouse Math. (5), 1, 77, 10.5802/afst.531
Triebel, 1983
Van Schaftingen, 2013, Limiting Sobolev inequalities for vector fields and canceling linear differential operators, J. Eur. Math. Soc., 15, 877, 10.4171/JEMS/380
Zhang, 1992, A construction of quasiconvex functions with linear growth at infinity, Ann. Sc. Norm. Super. Pisa, Cl. Sci. (4), 19, 313
