HOLDER CONTINUITY OF THE INVERSE OF P-LAPLACIAN

In this note, we study the inverse operator (-Delta(p))(-1) of p-Lapal cian on a bounded domain Omega subset of R-n. We show that (-Delta(p)) (-1):W--1,W-p'(Omega)-->W-0(1,p) (Omega) is Holder continuous and is a compact operator from V-(q,V-s) to W-0(1,p)(Omega), s is an element o f (0,p'), q > p the conjugate of critical Sobolev exponent. As an app lication, we study existence of positive solutions of two nonlinear el liptic equations. (C) 1998 Academic Press.