Details
| Original language | English |
|---|---|
| Pages (from-to) | 2215-2301 |
| Number of pages | 87 |
| Journal | Annales de l'Institut Fourier |
| Volume | 70 |
| Issue number | 5 |
| Publication status | Published - 2020 |
Abstract
We study the eigenvalues of the Laplacian with a strong attractive Robin boundary condition in curvilinear polygons. It was known from previous works that the asymptotics of several first eigenvalues is essentially determined by the corner openings, while only rough estimates were available for the next eigenvalues. Under some geometric assumptions, we go beyond the critical eigenvalue number and give a precise asymptotics of any individual eigenvalue by establishing a link with an effective Schrödinger-type operator on the boundary of the domain with boundary conditions at the corners.
Keywords
- Effective operator, Eigenvalue, Laplacian, Nonsmooth domain, Robin boundary condition
ASJC Scopus subject areas
- Mathematics(all)
- Geometry and Topology
- Mathematics(all)
- Algebra and Number Theory
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In: Annales de l'Institut Fourier, Vol. 70, No. 5, 2020, p. 2215-2301.
Research output: Contribution to journal › Article › Research
}
TY - JOUR
T1 - Effective operators for Robin eigenvalues in domains ith corners
AU - Khalile, Magda
AU - Pankrashkin, Konstantin
AU - Ourmières-Bonafos, Thomas
N1 - Funding Information: A large part of this paper was written while Thomas Ourmières-Bonafos was supported by a public grant as part of the “Investissement d’avenir” project, reference ANR-11-LABX-0056-LMH, LabEx LMH. Now, Thomas Ourmières-Bonafos is supported by the ANR “Défi des savoirs (DS10) 2017” programm, reference ANR-17-CE29-0004, project molQED. The initial version of the paper was significantly reworked following referee’s suggestions. We are very grateful to them for very constructive criticisms which resulted in a significant improvement of the text and in the inclusion of several additional results.
PY - 2020
Y1 - 2020
N2 - We study the eigenvalues of the Laplacian with a strong attractive Robin boundary condition in curvilinear polygons. It was known from previous works that the asymptotics of several first eigenvalues is essentially determined by the corner openings, while only rough estimates were available for the next eigenvalues. Under some geometric assumptions, we go beyond the critical eigenvalue number and give a precise asymptotics of any individual eigenvalue by establishing a link with an effective Schrödinger-type operator on the boundary of the domain with boundary conditions at the corners.
AB - We study the eigenvalues of the Laplacian with a strong attractive Robin boundary condition in curvilinear polygons. It was known from previous works that the asymptotics of several first eigenvalues is essentially determined by the corner openings, while only rough estimates were available for the next eigenvalues. Under some geometric assumptions, we go beyond the critical eigenvalue number and give a precise asymptotics of any individual eigenvalue by establishing a link with an effective Schrödinger-type operator on the boundary of the domain with boundary conditions at the corners.
KW - Effective operator
KW - Eigenvalue
KW - Laplacian
KW - Nonsmooth domain
KW - Robin boundary condition
UR - http://www.scopus.com/inward/record.url?scp=85107756259&partnerID=8YFLogxK
U2 - 10.5802/aif.3400
DO - 10.5802/aif.3400
M3 - Article
VL - 70
SP - 2215
EP - 2301
JO - Annales de l'Institut Fourier
JF - Annales de l'Institut Fourier
SN - 0373-0956
IS - 5
ER -