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

2017/03/10 by Gol'dshtein, V., Pchelintsev, V., Ukhlov, A.
#30C65 #35P15 #46E35 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1703.03577

Abstract

In this paper we study spectral properties of the Neumann-Laplace operator in planar quasiconformal regular domains Ω⊂\mathbb R². 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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