Work

Optimization of Neumann Eigenvalues Under Convexity and Geometric Constraints

Year: 2024

Type: article

Abstract: . In this paper we study optimization problems for Neumann eigenvalues [Formula: see text] among convex domains with a constraint on the diameter or the perimeter. We work mainly in the plane, though some results are stated in higher dimension. We study the existence of an optimal domain in all considered cases. We also consider the case of the unit disk, giving values of the index [Formula: see text] for which it can or cannot be extremal. We give some numerical examples for small values of [Formula: see text] that lead us to state some conjectures.

Source: SIAM Journal on Mathematical Analysis

DOI: 10.1137/24m1641099

Authors: Beniamin Bogosel, Antoine Henrot, Marco Michetti

Institutions: Centre National de la Recherche Scientifique, École Polytechnique, Centre de Mathématiques Appliquées de l'École polytechnique, Institut Polytechnique de Paris, Institut Élie Cartan de Lorraine, Université de Lorraine, Université Paris-Saclay, Laboratoire de Mathématiques d'Orsay

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4404079350

FWCI: 2.612

Cites: 25

Cited by: 4

Related to: 10