# Sobolev extension operators and Neumann eigenvalues

```@article{Goldshtein2017SobolevEO,
title={Sobolev extension operators and Neumann eigenvalues},
author={Vladimir Gol'dshtein and V. A. Pchelintsev and A. Ukhlov},
journal={Journal of Spectral Theory},
year={2017}
}```
• Published 16 October 2017
• Mathematics
• Journal of Spectral Theory
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).
1 Citations

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