Quasiconvexity and partial regularity via nonlinear potentials

被引：29

作者：

De Filippis, Cristiana ^{[1
]}

机构：

[1] Univ Parma, Dipartimento SMFI, Parco Area Sci 53-A, I-43124 Parma, Italy

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2022年 / 163卷

关键词：

Quasiconvexity; Nonlinear potential theory; Degenerate variational integrals; (p; q)-Growth; LOWER SEMICONTINUITY; MULTIPLE INTEGRALS; SINGULAR SET; MINIMIZERS; FUNCTIONALS; CALCULUS; APPROXIMATION; EQUATIONS; MINIMA; (P;

D O I：

10.1016/j.matpur.2022.05.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show how to infer sharp partial regularity results for relaxed minimizers of degenerate, nonuniformly elliptic quasiconvex functionals, using tools from Nonlinear Potential Theory. In particular, in the setting of functionals with (p, q)growth - according to the terminology of Marcellini [52] - we derive optimal local regularity criteria under minimal assumptions on the data. (c) 2022 Elsevier Masson SAS. All rights reserved.

引用

页码：11 / 82

页数：72

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