H¨older Continuity of the Inverse of p-Laplacian

In this note, we study the inverse operator yDp.y1 of p-Lapalcian on a n .y1 y1, pXbounded domain V;R . We show that yDp : W V.ªW01, p V. is H¨older continuous and is a compact operator from V q, s. to W01, p V., sg 0, pX., q )p# the conjugate of critical Sobolev exponent. As an application, we study existence of positive solutions of two nonlinear elliptic equations.