Work

Extrinsic bounds for the spectrum of a Steklov problem associated with the (p,q)-Laplacian

Year: 2025

Type: article

Abstract: A Steklov-like boundary problem associated with the (p, q)-Laplacian is considered in a bounded domain Ω ⊂ R n with a smooth boundary, where p, q ∈ (1, +∞) and p ̸ = q.It is known that the set of eigenvalues of this problem is {0} ∪ (λ1, +∞), where λ1 is a positive constant.The aim of the present article is to give upper bounds for λ1.These bounds are of two types: one based on the isoperimetric ratio and the other on the geometry of the boundary.Additionally, it is shown that if λ1 is close to any of these upper bounds, then Ω is close to a ball.

Source: Electronic Journal of Mathematics

DOI: 10.47443/ejm.2025.026

Author: Julien Roth

Institutions: Centre National de la Recherche Scientifique, Université Paris-Est Créteil, Laboratoire d’Analyse et de Mathématiques Appliquées, Université Gustave Eiffel

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4411366946

FWCI:

Cites: 1

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Related to: 10