Integral estimates of conformal derivatives and spectral properties of the Neumann-Laplacian

Integral estimates of conformal derivatives and spectral properties of the Neumann-Laplacian

Bibliographic Details
Parent link:Journal of Mathematical Analysis and Applications
Vol. 463, iss. 1.— 2018.— [P. 19-39]
Main Author: Go'ldshtein V. M. Vladimir
Corporate Author: Национальный исследовательский Томский политехнический университет Школа базовой инженерной подготовки Отделение математики и информатики
Other Authors: Pchelintsev V. A. Valery Anatoljevich, Ukhlov A. D. Alexander Dadaroolovich
Summary:Title screen
In this paper we study integral estimates of derivatives of conformal mappings φ:D→Ω of the unit disc D⊂C onto bounded domains Ω that satisfy the Ahlfors condition. These integral estimates lead to estimates of constants in Sobolev-Poincaré inequalities, and by the Rayleigh quotient we obtain spectral estimates of the Neumann-Laplace operator in non-Lipschitz domains (quasidiscs) in terms of the (quasi)conformal geometry of the domains. Specifically, the lower estimates of the first non-trivial eigenvalues of the Neumann-Laplace operator in some fractal type domains (snowflakes) were obtained.
Режим доступа: по договору с организацией-держателем ресурса
Published: 2018
Subjects:
электронный ресурс
Sobolev spaces
conformal mappings
quasiconformal mappings
elliptic equations
пространство Соболева
конформные отображения
квазиконформные отображения
эллиптические уравнения
труды учёных ТПУ
Online Access:https://doi.org/10.1016/j.jmaa.2018.02.063
Format: Electronic Book Chapter
KOHA link:https://koha.lib.tpu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=658512

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