Work

Optimisation and monotonicity of the second Robin eigenvalue on a planar exterior domain

Year: 2024

Type: article

Abstract: We consider the Laplace operator in the exterior of a compact set in the plane, subject to Robin boundary conditions. If the boundary coupling is sufficiently negative, there are at least two discrete eigenvalues below the essential spectrum. We state a general conjecture that the second eigenvalue is maximised by the exterior of a disk under isochoric or isoperimetric constraints. We prove an isoelastic version of the conjecture for the exterior of convex domains. Finally, we establish a monotonicity result for the second eigenvalue under the condition that the compact set is strictly star-shaped and centrally symmetric.

Source: Calculus of Variations and Partial Differential Equations

DOI: 10.1007/s00526-024-02824-3

Authors: David Krejčiřík, Vladimir Lotoreichik

Institutions: Czech Technical University in Prague, Czech Academy of Sciences, Czech Academy of Sciences, Nuclear Physics Institute

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funder: Grantová Agentura České Republiky