The Steklov Spectrum of Convex Polygonal Domains I: Spectral Finiteness
Journal article, 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
Author
Emily B. Dryden
Bucknell University
Carolyn Gordon
Dartmouth College
Javier Moreno
University of Los Andes
Julie Rowlett
Chalmers, Mathematical Sciences, Analysis and Probability Theory
University of Gothenburg
Carlos Villegas-Blas
Universidad Nacional Autónoma de México
Journal of Geometric Analysis
1050-6926 (ISSN)
Vol. 35 3 91Subject Categories (SSIF 2025)
Mathematical Analysis
DOI
10.1007/s12220-025-01922-8