Nonlinear elliptic boundary value problem with equivalued surface in a domain with thin layer

Abstract

Abstract. This paper deals with certain kinds of boundary value problems with equivalued surface of nonlinear elliptic equations on a domain with thin layer. We introduce the concept of renormalized solution to this problem. Existence and uniqueness of renormalized solutions are given, and the limit behaviour of solutions is studied in this paper. Mathematics Subject Classification (2000). 35B37, 35B40, 49J20.