The Steklov Spectrum of Convex Polygonal Domains I: Spectral Finiteness
Artikel i vetenskaplig tidskrift, 2025

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.

Steklov

Curvilinear polygon

Eigenvalues

Inverse spectral problem

Dirichlet-to-Neumann map

Polygon

Författare

Emily B. Dryden

Bucknell University

Carolyn Gordon

Dartmouth College

Javier Moreno

Universidad de los Andes

Julie Rowlett

Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori

Göteborgs universitet

Carlos Villegas-Blas

Universidad Nacional Autónoma de México

Journal of Geometric Analysis

1050-6926 (ISSN)

Vol. 35 3 91

Ämneskategorier (SSIF 2025)

Matematisk analys

DOI

10.1007/s12220-025-01922-8

Mer information

Senast uppdaterat

2025-02-28