On growth monotonicity estimates of the principal Dirichlet-Laplacian eigenvalue

TL;DR

This paper develops growth monotonicity estimates for the principal Dirichlet-Laplacian eigenvalue in complex domains using quasiconformal mappings and weighted Sobolev inequalities, advancing spectral theory in irregular geometries.

Contribution

It introduces a novel approach employing composition operators and quasiconformal mappings to estimate eigenvalues in non-Lipschitz domains.

Findings

Established growth monotonicity estimates for eigenvalues

Applied composition operators to spectral problems

Extended spectral analysis to irregular domains

Abstract

In the present paper we obtain growth monotonicity estimates of the principal Dirichlet-Laplacian eigenvalue in bounded non-Lipschitz domains. The proposed method is based on composition operators generated by quasiconformal mappings and their applications to weighted Sobolev inequalities.