Lipschitz continuity for energy integrals with variable exponents

被引：50

作者：

Eleuteri, Michela ^{[1
]}

Marcellini, Paolo ^{[1
]}

Mascolo, Elvira ^{[1
]}

机构：

[1] Univ Florence, Dipartimento Matemat & Informat U Dini, Viale Morgagni 67-A, I-50134 Florence, Italy

来源：

RENDICONTI LINCEI-MATEMATICA E APPLICAZIONI | 2016年 / 27卷 / 01期

关键词：

Energy integrals; local minimizers; local Lipschitz continuity; p(x)-growth; variable exponents; ELLIPTIC-EQUATIONS; HOLDER CONTINUITY; REGULARITY; FUNCTIONALS; MINIMIZERS; CALCULUS; GRADIENT;

D O I：

10.4171/RLM/723

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A regularity result for integrals of the Calculus of Variations with variable exponents is presented. Precisely, we prove that any vector-valued minimizer of an energy integral over an open set Omega subset of R-n, with variable exponent p(x) in the Sobolev class W-loc(1, r)(Omega) for some r > n, is locally Lipschitz continuous in Omega and an a priori estimate holds.

引用

页码：61 / 87

页数：27

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