@inbook{79d74139884b42949be22fc3ae1b0b7f,
title = "Spectral properties of the neumann-laplace operator in quasiconformal regular domains",
abstract = "In this paper we study spectral properties of the Neumann-Laplace operator in planar quasiconformal regular domains Ω ⊂ ℝ2 . This study is based on the quasiconformal theory of composition operators on Sobolev spaces. We obtain estimates of constants in Poincar{\'e}-Sobolev inequalities and as a consequence lower estimates of the first non-trivial eigenvalue of the Neumann-Laplace operator in planar quasiconformal regular domains.",
keywords = "And phrases, Elliptic equations, Quasiconformal mappings, Sobolev spaces",
author = "V. Gol{\textquoteright}dshtein and V. Pchelintsev and A. Ukhlov",
note = "Publisher Copyright: {\textcopyright}2019 American Mathematical Society.",
year = "2019",
month = jan,
day = "1",
doi = "10.1090/conm/734/14768",
language = "English",
series = "Contemporary Mathematics",
publisher = "American Mathematical Society",
pages = "129--144",
booktitle = "Contemporary Mathematics",
address = "United States",
}