Journal of Inequalities and Applications 
Volume 2008 (2008), Article ID 835736, 12 pages
doi:10.1155/2008/835736
Research Article

Local Regularity Results for Minima of Anisotropic Functionals and Solutions of Anisotropic Equations

Gao Hongya,1,2 Qiao Jinjing,1 Wang Yong,3 and Chu Yuming4

 1College of Mathematics and Computer Science, Hebei University, Baoding 071002, China
2Study Center of Mathematics of Hebei Province, Shijiazhuang 050016, China
3Department of Mathematics, Chengde Teachers College for Nationalities, Chengde 067000, China
4Faculty of Science, Huzhou Teachers College, Huzhou 313000, China
Received 13 July 2007; Accepted 21 November 2007

Recommended by Alberto Cabada

Abstract

This paper gives some local regularity results for minima of anisotropic functionals I(u;Ω)=∫Ωf(x,u,Du)dx, u∈Wloc1,qi(Ω) and for solutions of anisotropic equations −div𝒜(x,u,Du)=-∑i=1N(∂f/∂xi), u∈Wloc1,qi(Ω) which can be regarded as generalizations of the classical results.