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arXiv · 1104.5264

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

Andrea Posilicano
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Abstract

By Birman and Skvortsov it is known that if $\Omegasf$ is a planar curvilinear polygon with $n$ non-convex corners then the Laplace operator with domain $H^2(\Omegasf)\cap H^1_0(\Omegasf)$ is a closed symmetric operator with deficiency indices $(n,n)$. Here we provide a Kre\uın-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 $\Omegasf$, 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.

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Andrea Posilicano. 2013-05-10. On the many Dirichlet Laplacians on a non-convex polygon and their approximations by point interactions. https://doi.org/10.1016/j.jfa.2013.05.013

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