Regularity results for a new class of functionals with non-standard growth conditions

被引：55

作者：

Giannetti, Flavia ^{[1
]}

di Napoli, Antonia Passarelli ^{[1
]}

机构：

[1] Univ Naples Federico II, Dipartimento Matemat & Applicaz R Caccioppoli, I-80126 Naples, Italy

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2013年 / 254卷 / 03期

关键词：

Variational integrals; Variable exponents; Holder regularity; HIGHER INTEGRABILITY; ELLIPTIC-EQUATIONS; HOLDER CONTINUITY; MINIMIZERS; INTEGRALS; GRADIENT;

D O I：

10.1016/j.jde.2012.10.011

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that local minimizers of the functional F(u) := integral(Omega) vertical bar Du vertical bar(p(x)) log (e + vertical bar Du vertical bar)dx are of class C-0,C-alpha for every 0 < alpha < 1, if the exponent p(x) > 1 has logarithmic modulus of continuity. Moreover, in case the exponent p(x) > 1 is a Holder continuous function, we establish that minimizers of F(u) are of class C-1,C-alpha, for some 0 < alpha < 1. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：1280 / 1305

页数：26

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