Mathematica Eterna
Open Access

Abstract

Local Regularity for Minimizers of Obstacle Problems of Some Anisotropic Integral Functionals

GAO Hongya, GAO Yanmin, GUO Kaili and JIA miaomiao

A local regularity result is obtained for minimizers u ∈ Kψ = n u ∈ W 1,(qi) loc (Ω) : u ≥ ψ}, qi > 1, ∀i = 1, · · · , N, of anisotropic integral functionals of the type F(u; Ω) = Z Ω f(x, u, Du)dx, where the Carath´eodory function f(x, u, Du) = f0(x, u, Du)+f1(x, u, Du), f0(x, s, z) grows like PN i=1 |zi | qi , and f1(x, s, z) satisfies some controllable growth condition.