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arXiv · 1703.03577

Spectral Properties of the Neumann-Laplace operator in Quasiconformal Regular Domains

V. Gol'dshtein·V. Pchelintsev·A. Ukhlov
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Abstract

In this paper we study spectral properties of the Neumann-Laplace operator in planar quasiconformal regular domains $Ω\subset\mathbb R^2$. This study is based on the quasiconformal theory of composition operators on Sobolev spaces. Using the composition operators theory we obtain estimates of constants in Poincaré-Sobolev inequalities and as a consequence lower estimates of the first non-trivial eigenvalue of the Neumann-Laplace operator in planar quasiconformal regular domains.

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V. Gol'dshtein, V. Pchelintsev, A. Ukhlov. 2017-03-10. Spectral Properties of the Neumann-Laplace operator in Quasiconformal Regular Domains. https://arxiv.org/abs/1703.03577

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