Lower semicontinuity and relaxation for free discontinuity functionals with non-standard growth

被引：5
作者：
Almi, Stefano [1 ]
Reggiani, Dario [2 ]
Solombrino, Francesco [1 ]
机构：
[1] Univ Napoli Federico II, Dipartimento Matemat & Applicaz R Caccioppoli, Via Cintia, I-80126 Naples, Italy
[2] Univ Napoli Federico II, Scuola Super Meridionale, Largo San Marcellino 10, I-80138 Naples, Italy
来源：
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2024年 / 63卷 / 01期
基金：
奥地利科学基金会;
关键词：
49J45; 46E30; 49M20; QUASI-CONVEX INTEGRALS; VARIABLE EXPONENT; MULTIPLE INTEGRALS; GAMMA-CONVERGENCE; GLOBAL METHOD; REGULARITY; MINIMIZERS; EXISTENCE; GRADIENT; SBV;
D O I：
10.1007/s00526-023-02623-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A lower semicontinuity result and a relaxation formula for free discontinuity functionals with non-standard growth in the bulk energy are provided. Our analysis is based on a non-trivial adaptation of the blow-up (Ambrosio in Nonlinear Anal 23:405-425, 1994) and of the global method for relaxation (Bouchitte in Arch Ration Mech Anal 165:187-242, 2002) to the setting of generalized special function of bounded variation with Orlicz growth. Key tools developed in this paper are an integral representation result and a Poincare inequality under non-standard growth.
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页数：58
相关论文
共 70 条
[41]   Global gradient estimates for the p(•)-Laplacian [J].
Diening, L. ;
Schwarzacher, S. .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2014, 106 :70-85
[42]   PARTIAL REGULARITY FOR MINIMIZERS OF QUASI-CONVEX FUNCTIONALS WITH GENERAL GROWTH [J].
Diening, L. ;
Lengeler, D. ;
Stroffolini, B. ;
Verde, A. .
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2012, 44 (05) :3594-3616
[43]   Lipschitz regularity of minimizers of variational integrals with variable exponents [J].
Eleuteri, Michela ;
di Napoli, Antonia Passarelli .
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2023, 71
[44]  
Evans L.C., 2015, Measure Theory and Fine Properties of Functions, Vrevised
[45]   A-quasiconvexity:: weak-star convergence and the gap [J].
Fonseca, I ;
Leoni, G ;
Müller, S .
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2004, 21 (02) :209-236
[46]   Relaxation of multiple integrals below the growth exponent [J].
Fonseca, I ;
Maly, J .
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 1997, 14 (03) :309-338
[47]  
Gmeineder F, 2022, Arxiv, DOI arXiv:2209.01613
[48]  
Harjulehto P, 2004, ANN ACAD SCI FENN-M, V29, P295
[49]   Critical variable exponent functionals in image restoration [J].
Harjulehto, P. ;
Hasto, P. ;
Latvala, V. ;
Toivanen, O. .
APPLIED MATHEMATICS LETTERS, 2013, 26 (01) :56-60
[50]   Minimizers of the variable exponent, non-uniformly convex Dirichlet energy [J].
Harjulehto, Petteri ;
Hasto, Peter ;
Latvala, Visa .
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2008, 89 (02) :174-197
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