Global gradient estimates for nonlinear equations of p-Laplace type from composite materials

Abstract

We study global gradient estimates for the weak solution to divergence form nonlinear elliptic equations with p -growth nonlinearities from composite materials. We assume that the domain is bounded and is composed of disjoint Reifenberg flat domains and the nonlinearities have small BMO seminorms in each subdomain. Under these assumptions, based on our new geometric observation for disjoint Reifenberg domains and gradient estimates for nonlinear equations with measurable p -growth nonlinearities, we establish global W 1 , q estimates for p ≤ q < ∞ .