THE INITIAL DIRICHLET BOUNDARY VALUE PROBLEM FOR GENERAL SECOND ORDER PARABOLIC SYSTEMS IN NONSMOOTH MANIFOLDS

Abstract

We consider some unilateral boundary value problems in polygonal and polyhedral domains with unilateral transmission conditions. Regularity results in terms of weighted Sobolev spaces are obtained using a penalization technique, similar regularity results for the penalized problems and by showing uniform estimates with respect to the penalization parameter.