Composition Operators on Sobolev Spaces and Neumann Eigenvalues

V. Gol’dshtein; A. Ukhlov

doi:10.1007/s11785-018-0826-1

Composition Operators on Sobolev Spaces and Neumann Eigenvalues

V. Gol’dshtein, A. Ukhlov

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

In this paper we discuss applications of the geometric theory of composition operators on Sobolev spaces to the spectral theory of non-linear elliptic operators. Lower estimates of the first non-trivial Neumann eigenvalues of the p-Laplace operator in cusp domains Ω ⊂ Rⁿ, n≥ 2 , are given.

Original language	English
Pages (from-to)	2781-2798
Number of pages	18
Journal	Complex Analysis and Operator Theory
Volume	13
Issue number	6
DOIs	https://doi.org/10.1007/s11785-018-0826-1
State	Published - 1 Sep 2019

Keywords

Neumann eigenvalues
Quasiconformal mappings
Sobolev spaces

ASJC Scopus subject areas

Computational Mathematics
Computational Theory and Mathematics
Applied Mathematics

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10.1007/s11785-018-0826-1

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title = "Composition Operators on Sobolev Spaces and Neumann Eigenvalues",

abstract = "In this paper we discuss applications of the geometric theory of composition operators on Sobolev spaces to the spectral theory of non-linear elliptic operators. Lower estimates of the first non-trivial Neumann eigenvalues of the p-Laplace operator in cusp domains Ω ⊂ Rn, n≥ 2 , are given.",

keywords = "Neumann eigenvalues, Quasiconformal mappings, Sobolev spaces",

author = "V. Gol{\textquoteright}dshtein and A. Ukhlov",

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year = "2019",

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doi = "10.1007/s11785-018-0826-1",

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AU - Ukhlov, A.

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N2 - In this paper we discuss applications of the geometric theory of composition operators on Sobolev spaces to the spectral theory of non-linear elliptic operators. Lower estimates of the first non-trivial Neumann eigenvalues of the p-Laplace operator in cusp domains Ω ⊂ Rn, n≥ 2 , are given.

AB - In this paper we discuss applications of the geometric theory of composition operators on Sobolev spaces to the spectral theory of non-linear elliptic operators. Lower estimates of the first non-trivial Neumann eigenvalues of the p-Laplace operator in cusp domains Ω ⊂ Rn, n≥ 2 , are given.

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KW - Quasiconformal mappings

KW - Sobolev spaces

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M3 - Article

AN - SCOPUS:85051662137

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JO - Complex Analysis and Operator Theory

JF - Complex Analysis and Operator Theory

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ER -

Composition Operators on Sobolev Spaces and Neumann Eigenvalues

Abstract

Keywords

ASJC Scopus subject areas

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