Local behavior of fractional p-minimizers

Agnese Di Castro1,2, Tuomo Kuusi3, Giampiero Palatucci1,4
1Dipartimento di Matematica e Informatica, Università degli Studi di Parma, Campus—Parco Area delle Scienze 53/A, 43124 Parma, Italy
2Dipartimento SBAI, Sapienza, Università di Roma, Via Scarpa 16, 00161 Roma, Italy
3Department of Mathematics and Systems Analysis, Aalto University, P.O. Box 1100, 00076 Aalto, Finland
4SISSA, Via Bonomea 256, 34136 Trieste, Italy

Tài liệu tham khảo

Bjorland, 2012, Non-local gradient dependent operators, Adv. Math., 230, 1859, 10.1016/j.aim.2012.03.032 Brasco Chambolle, 2012, A Hölder infinity Laplacian, ESAIM Control Optim. Calc. Var., 18, 799, 10.1051/cocv/2011182 Caffarelli, 2007, An extension problem related to the fractional Laplacian, Commun. Partial Differ. Equ., 32, 1245, 10.1080/03605300600987306 Da Lio, 2011, 3-commutators estimates and the regularity of 1/2-harmonic maps into spheres, Anal. PDE, 4, 149, 10.2140/apde.2011.4.149 De Giorgi, 1957, Sulla differenziabilità e l'analiticità delle estremali degli integrali multipli regolari, Mem. Accad. Sci. Torino, Cl. Sci. Fis. Mat. Nat., 3, 25 Di Castro, 2014, Nonlocal Harnack inequalities, J. Funct. Anal., 267, 1807, 10.1016/j.jfa.2014.05.023 Di Nezza, 2012, Hitchhiker's guide to the fractional Sobolev spaces, Bull. Sci. Math., 136, 521, 10.1016/j.bulsci.2011.12.004 Franzina, 2014, Fractional p-eigenvalues, Riv. Mat. Univ. Parma, 5, 315 Kassmann, 2007 Kassmann Kassmann, 2009, A priori estimates for integro-differential operators with measurable kernels, Calc. Var. Partial Differ. Equ., 34, 1, 10.1007/s00526-008-0173-6 Kassmann Kuusi, 2015, Nonlocal equations with measure data, Commun. Math. Phys., 337, 1317, 10.1007/s00220-015-2356-2 Iannizzotto, 2015, Existence results for fractional p-Laplacian problems via Morse theory, Adv. Calc. Var. Ishii, 2010, A class of integral equations and approximation of p-Laplace equations, Calc. Var. Partial Differ. Equ., 37, 485, 10.1007/s00526-009-0274-x Lindgren Lindgren, 2014, Fractional eigenvalues, Calc. Var. Partial Differ. Equ., 49, 795, 10.1007/s00526-013-0600-1 Malý, 1997 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, 2007, The Calderón–Zygmund theory for elliptic problems with measure data, Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5), 6, 195 Mingione, 2011, Gradient potential estimates, J. Eur. Math. Soc., 13, 459 Moser, 1961, On Harnack's theorem for elliptic differential equations, Commun. Pure Appl. Math., 14, 577, 10.1002/cpa.3160140329 Nash, 1958, Continuity of solutions of parabolic and elliptic equations, Am. J. Math., 80, 931, 10.2307/2372841 Palatucci, 2014, Improved Sobolev embeddings, profile decomposition, and concentration-compactness for fractional Sobolev spaces, Calc. Var. Partial Differ. Equ., 50, 799, 10.1007/s00526-013-0656-y Palatucci, 2013, Local and global minimizers for a variational energy involving a fractional norm, Ann. Mat. Pura Appl. (4), 192, 673, 10.1007/s10231-011-0243-9 G. Palatucci, A. Pisante, Y. Sire, Subcritical approximation of a Yamabe type non local equation: a Gamma-convergence approach, Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5), http://dx.doi.org/10.2422/2036-2145.201302_006. Savin, 2011, Density estimates for a nonlocal variational model via the Sobolev inequality, SIAM J. Math. Anal., 43, 2675, 10.1137/110831040 Savin, 2014, Density estimates for a variational model driven by the Gagliardo norm, J. Math. Pures Appl., 101, 1, 10.1016/j.matpur.2013.05.001 Servadei, 2014, Weak and viscosity solutions of the fractional Laplace equation, Publ. Mat., 58, 133, 10.5565/PUBLMAT_58114_06 Silvestre, 2006, Hölder estimates for solutions of integro-differential equations like the fractional Laplace, Indiana Univ. Math. J., 55, 1155, 10.1512/iumj.2006.55.2706