Laplacians with singular perturbations supported on hypersurfaces
https://doi.org/10.17586/2220-8054-2016-7-2-315-323
Abstract
We review the main results of our recent work on singular perturbations supported on bounded hypersurfaces. Our approach consists in using the theory of self-adjoint extensions of restrictions to build self-adjoint realizations of the n-dimensional Laplacian with linear boundary conditions on (a relatively open part of) a compact hypersurface. This allows one to obtain Kreın-like resolvent formulae where the reference operator coincides with the free selfadjoint Laplacian in Rn, providing in this way with an useful tool for the scattering problem from a hypersurface. As examples of this construction, we consider the cases of Dirichlet and Neumann boundary conditions assigned on an unclosed hypersurface.
About the Authors
A. Mantile
Laboratoire de Math´ematiques de Reims; F´ed´eration de Recherche ARC Math´ematiques
France
France
EA4535 URCA
FR 3399 CNRS
A. Posilicano
DiSAT, Sezione di Matematica, Universit`a dell’Insubria
Italy
Italy
via Valleggio 11, I-22100 Como
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Review
For citations:
Mantile A., Posilicano A. Laplacians with singular perturbations supported on hypersurfaces. Nanosystems: Physics, Chemistry, Mathematics. 2016;7(2):315-323. https://doi.org/10.17586/2220-8054-2016-7-2-315-323
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