Spectral Convergence of the Laplace Operator with Robin Boundary Conditions on a Small Hole

0578402 - ÚJF 2024 RIV CH eng J - Journal Article
Barseghyan, Diana - Schneider, B.
Spectral Convergence of the Laplace Operator with Robin Boundary Conditions on a Small Hole.
Mediterranean Journal of Mathematics. Roč. 20, č. 6 (2023), č. článku 304. ISSN 1660-5446. E-ISSN 1660-5454
R&D Projects: GA ČR(CZ) GA21-07129S
Institutional support: RVO:61389005
Keywords : Robin Laplacian * spectral convergence * domain with a hole
OECD category: Applied mathematics
Impact factor: 1.1, year: 2022
Method of publishing: Open access
https://doi.org/10.1007/s00009-023-02510-2

In this paper, we study a bounded domain with a small hole removed. Our main result concerns the spectrum of the Laplace operator with the Robin conditions imposed at the hole boundary. Moreover, we prove that under some suitable assumptions on the parameter in the boundary condition, the spectrum of the Laplacian converges in the Hausdorff distance sense to the spectrum of the Laplacian defined on the unperturbed domain.
Permanent Link: https://hdl.handle.net/11104/0347398