Sobolev Extension Operators and Neumann Eigenvalues

2017/10/16 by Gol'dshtein, V., Pchelintsev, V., Ukhlov, A. · 1 citation
#30C65 #35P15 #46E35 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1710.05560

Abstract

In this paper we apply estimates of the norms of Sobolev extension operators to the spectral estimates of of the first nontrivial Neumann eigenvalue of the Laplace operator in non-convex extension domains. As a consequence we obtain a connection between resonant frequencies of free membranes and the smallest-circle problem (initially proposed by J.~J.~Sylvester in 1857).

Cited by

• Estimates of variational eigenvalues on metric measure spaces

Related

• The spectral estimates for the Neumann-Laplace operator in space domains
• Principal frequencies of free non-homogeneous membranes and Sobolev extension operators
• Sobolev (p,q)-extension operators and Neumann eigenvalues
• Lower bounds on the norms of extension operators for Lipschitz domains
• Composition Operators on Sobolev Spaces and Neumann Eigenvalues