Spectral estimates of the p-Laplace Neumann operator and Brennan’s conjecture

Vladimir Gol’dshtein; Valerii Pchelintsev; Alexander Ukhlov

doi:10.1007/s40574-017-0127-z

Spectral estimates of the p-Laplace Neumann operator and Brennan’s conjecture

Vladimir Gol’dshtein, Valerii Pchelintsev, Alexander Ukhlov

Department of Mathematics

Ben-Gurion University of the Negev

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

Abstract

In this paper we obtain lower estimates for the first non-trivial eigenvalue of the p-Laplace Neumann operator in bounded simply connected planar domains Ω⊂ R². This study is based on a quasiconformal version of the universal two-weight Poincaré–Sobolev inequalities obtained in our previous papers for conformal weights and its non weighted version for so-called K-quasiconformal α-regular domains. The main technical tool is the geometric theory of composition operators in relation with the Brennan’s conjecture for (quasi)conformal mappings.

Original language	American English
Pages (from-to)	245-264
Number of pages	20
Journal	Bolletino dell Unione Matematica Italiana
Volume	11
Issue number	2
DOIs	https://doi.org/10.1007/s40574-017-0127-z
State	Published - 1 Jun 2018

Keywords

Elliptic equations
Quasiconformal mappings
Sobolev spaces

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s40574-017-0127-z

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abstract = "In this paper we obtain lower estimates for the first non-trivial eigenvalue of the p-Laplace Neumann operator in bounded simply connected planar domains Ω⊂ R2. This study is based on a quasiconformal version of the universal two-weight Poincar{\'e}–Sobolev inequalities obtained in our previous papers for conformal weights and its non weighted version for so-called K-quasiconformal α-regular domains. The main technical tool is the geometric theory of composition operators in relation with the Brennan{\textquoteright}s conjecture for (quasi)conformal mappings.",

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AU - Gol’dshtein, Vladimir

AU - Pchelintsev, Valerii

AU - Ukhlov, Alexander

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Y1 - 2018/6/1

N2 - In this paper we obtain lower estimates for the first non-trivial eigenvalue of the p-Laplace Neumann operator in bounded simply connected planar domains Ω⊂ R2. This study is based on a quasiconformal version of the universal two-weight Poincaré–Sobolev inequalities obtained in our previous papers for conformal weights and its non weighted version for so-called K-quasiconformal α-regular domains. The main technical tool is the geometric theory of composition operators in relation with the Brennan’s conjecture for (quasi)conformal mappings.

AB - In this paper we obtain lower estimates for the first non-trivial eigenvalue of the p-Laplace Neumann operator in bounded simply connected planar domains Ω⊂ R2. This study is based on a quasiconformal version of the universal two-weight Poincaré–Sobolev inequalities obtained in our previous papers for conformal weights and its non weighted version for so-called K-quasiconformal α-regular domains. The main technical tool is the geometric theory of composition operators in relation with the Brennan’s conjecture for (quasi)conformal mappings.

KW - Elliptic equations

KW - Quasiconformal mappings

KW - Sobolev spaces

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EP - 264

JO - Bolletino dell Unione Matematica Italiana

JF - Bolletino dell Unione Matematica Italiana

IS - 2

ER -

Spectral estimates of the p-Laplace Neumann operator and Brennan’s conjecture

Abstract

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