Sobolev Extension Operators and Neumann Eigenvalues
Analysis of PDEs
2017-10-17 v1
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).
Keywords
Cite
@article{arxiv.1710.05560,
title = {Sobolev Extension Operators and Neumann Eigenvalues},
author = {V. Gol'dshtein and V. Pchelintsev and A. Ukhlov},
journal= {arXiv preprint arXiv:1710.05560},
year = {2017}
}
Comments
12 pages