Regularity of the Solution of Some Unilateral Boundary Value Problems in Polygonal and Polyhedral Domains

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.

Keywords:

• AMS Subject Classification:35J85
• 35J25
• 35B65
• 49N60
• 35J60