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}
}
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). 
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