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.

引用

页数：58

共 70 条

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