A priori estimate for non-uniform elliptic equations

Abstract

A priori estimate for non-uniform elliptic equations with periodic boundary conditions is concerned. The domain considered consists. of two sub-regions, a connected high permeability region and a disconnected matrix block region with low permeability. Let c denote the size ratio of one matrix block to the whole domain. It is shown that in the connected high permeability sub-region, the Holder and the Lipschitz estimates of the non-uniform elliptic solutions are bounded uniformly in epsilon. But Holder gradient estimate and L(P) estimate of the second order derivatives of the solutions in general are not bounded uniformly in epsilon. (c) 2010 Elsevier Inc. All rights reserved.