On the First Eigenvalue of the Degenerate pp -Laplace Operator in Non-convex Domains; Integral Equations and Operator Theory; Vol. 90, iss. 4

On the First Eigenvalue of the Degenerate pp -Laplace Operator in Non-convex Domains; Integral Equations and Operator Theory; Vol. 90, iss. 4

Bibliographic Details
Parent link:Integral Equations and Operator Theory
Vol. 90, iss. 4.— 2018.— [43, 21 p.]
Main Author: Gol’dshtein 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 obtain lower estimates of the first non-trivial eigenvalues of the degenerate p-Laplace operator, p>2 , in a large class of non-convex domains. This study is based on applications of the geometric theory of composition operators on Sobolev spaces that permits us to estimate constants of the Poincare–Sobolev inequalities. On this base we obtain lower estimates of the first non-trivial eigenvalues for Ahlfors-type domains (i.e. quasidiscs). This class of domains includes some snowflake-type domains with fractal boundaries.
Режим доступа: по договору с организацией-держателем ресурса
Language:English
Published: 2018
Subjects:
электронный ресурс
труды учёных ТПУ
elliptic equations
Sobolev spaces
эллиптические уравнения
пространство Соболева
квазиконформные отображения
операторы
Composition operators
Online Access:https://doi.org/10.1007/s00020-018-2469-z
Format: Electronic Book Chapter
KOHA link:https://koha.lib.tpu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=659586
Description
Summary:Title screen
In this paper we obtain lower estimates of the first non-trivial eigenvalues of the degenerate p-Laplace operator, p>2 , in a large class of non-convex domains. This study is based on applications of the geometric theory of composition operators on Sobolev spaces that permits us to estimate constants of the Poincare–Sobolev inequalities. On this base we obtain lower estimates of the first non-trivial eigenvalues for Ahlfors-type domains (i.e. quasidiscs). This class of domains includes some snowflake-type domains with fractal boundaries.
Режим доступа: по договору с организацией-держателем ресурса
DOI:10.1007/s00020-018-2469-z

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