On growth monotonicity estimates of the principal Dirichlet-Laplacian eigenvalue

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.

10 pages

References in corpus (2)

• On the First Eigenvalues of Free Vibrating Membrane in Conformal Regular Domains
• Conformal spectral stability for the Dirichlet-Laplace operator