The Steklov Spectrum of Convex Polygonal Domains I: Spectral Finiteness
Abstract We explore the Steklov eigenvalue problem on convex polygons, focusing mainly on the inverse Steklov problem. Our primary finding reveals that, for almost all convex polygonal domains, there exist at most finitely many non-congruent domains with the same Steklov spectrum. Moreover, we obtain explicit upper bounds for the maximum number of mutually Steklov isospectral non-congruent polygonal domains. Along the way, we obtain isoperimetric bounds for the Steklov eigenvalues of a convex polygon in terms of the minimal interior angle of the polygon.
Authors
- Carolyn S. Gordon (ORCID: https://orcid.org/0000-0001-6626-631X)
- Julie Rowlett (ORCID: https://orcid.org/0000-0002-5724-3252)
- Emily B. Dryden
- Carlos Villegas‐Blas (ORCID: https://orcid.org/0000-0003-2467-9284)
- Javier Moreno (ORCID: https://orcid.org/0000-0002-9949-4412)
Institutions
- Dartmouth College (US)
- Bucknell University (US)
- Universidad de Los Andes (CO)
- Instituto Nacional de Salud Pública (MX)
- Chalmers University of Technology (SE)
- Universidad Autónoma del Estado de Morelos (MX)
- Universidad Nacional Autónoma de México (MX)
Publication Details
- Journal
- Journal of Geometric Analysis
- Published
- 2025-02-06
- DOI
- https://doi.org/10.1007/s12220-025-01922-8
- Primary Topic
- Mathematical Analysis and Transform Methods
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Chalmers Tekniska Högskola
- Consejo Nacional de Ciencia y Tecnología