Local Regularity and Local Boundedness Results for Very Weak Solutions of Obstacle Problems

Abstract

Local regularity and local boundedness results for very weak solutions of obstacle problems of the 𝒜-harmonic equation div⁡𝒜(x,∇u(x))=0 are obtained by using the theory of Hodge decomposition, where |𝒜(x,ξ)|≈|ξ|p-1.