On the many Dirichlet Laplacians on a non-convex polygon and their approximations by point interactions

Original · EN

By Birman and Skvortsov it is known that if is a planar curvilinear polygon with n non-convex corners then the Laplace operator with domain H²()∩ H¹₀() is a closed symmetric operator with deficiency indices (n,n). Here we provide a Kreın-type resolvent formula for any self-adjoint extensions of such an operator, i.e. for the set of self-adjoint non-Friedrichs Dirichlet Laplacians on, and show that any element in this set is the norm resolvent limit of a suitable sequence of Friedrichs-Dirichlet Laplacians with n point interactions.