Spectral properties of the Neumann-Laplace operator in quasiconformal regular domains

@article{Goldshtein2019SpectralPO,
  title={Spectral properties of the Neumann-Laplace
 operator in quasiconformal regular domains},
  author={Vladimir Gol'dshtein and V. A. Pchelintsev and A. Ukhlov},
  journal={Contemporary Mathematics},
  year={2019}
}
In this paper we study spectral properties of the Neumann-Laplace operator in planar quasiconformal regular domains $\Omega\subset\mathbb R^2$. 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 Poincare-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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