Mathematica Eterna
Open Access

Abstract

Local Regularity for Minimizers of Obstacle Problems of Some Integral Functionals

GAO Hongya, GUO Kaili, GAO Yanmin and JIA miaomiao

A local regularity result is obtained for minimizers u ∈ Kψ = n u ∈ W 1,p loc (Ω) : u ≥ ψ}, 1 < p < ∞, of 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 |z| p with 1 < p < ∞, and f1(x, s, z) satisfies some controllable growth condition.