Partial regularity of minimizers of p(x)-growth functionals with p(x) > 1

被引：3
作者：
Nio, Erika [1 ]
Usuba, Kunihiro [1 ]
机构：
[1] Tokyo Univ Sci, Fac Sci & Technol, Dept Math, Noda, Chiba 2788510, Japan
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2017年 / 156卷
关键词：
Variational integral; Minimizer; Non-standard growth; Variable exponent; Lower order term; GENERAL GROWTH-CONDITIONS; NON-STANDARD GROWTH; BOUNDARY-REGULARITY; P(X)-ENERGY FUNCTIONALS; QUADRATIC FUNCTIONALS; VARIATIONAL INTEGRALS; ELLIPTIC-EQUATIONS; HOLDER CONTINUITY; MINIMA; MAPS;
D O I：
10.1016/j.na.2017.01.020
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove partial regularity of minimizers u for functionals of the following type A(u) = integral(ohm)[(Alpha(alpha beta)(ij)(x,u,)D(alpha)u(i) D(beta)u(j))(p(x)/2) + g(x,u,Du)] dx, assuming that Alpha(alpha beta)(ij)(x, u) and p(x) are sufficiently smooth and that p(x) > 1. We prove that u is an element of C-0,C-alpha(ohm(0)) for some alpha is an element of (0,1) and an open set ohm(0) C ohm with Eta(m-n)(ohm - ohm(0)) = 0, where Eta(s) denotes the s -dimensional Hausdorff measure and gamma(1) = inf ohm p(x). (C) 2017 Elsevier Ltd. All rights reserved.
引用
收藏
页码：197 / 214
页数：18
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