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

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.