Space quasiconformal composition operators with applications to Neumann eigenvalues

Vladimir Gol’dshtein; Ritva Hurri-Syrjänen; Valerii Pchelintsev; Alexander Ukhlov

doi:10.1007/978-3-031-25424-6_6

Space quasiconformal composition operators with applications to Neumann eigenvalues

Vladimir Gol’dshtein, Ritva Hurri-Syrjänen, Valerii Pchelintsev, Alexander Ukhlov

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

In this article we obtain estimates of Neumann eigenvalues of p-Laplace operators in a large class of space domains satisfying quasihyperbolic boundary conditions. The suggested method is based on composition operators generated by quasiconformal mappings and their applications to Sobolev–Poincaré-inequalities. By using a sharp version of the reverse Hölder inequality we refine our estimates for quasi-balls, that is, images of balls under quasiconformal mappings of the whole space.

Original language	English
Title of host publication	Harmonic Analysis and Partial Differential Equations
Subtitle of host publication	In Honor of Vladimir Maz'ya
Publisher	Springer Nature
Pages	141-160
Number of pages	20
ISBN (Electronic)	9783031254246
ISBN (Print)	9783031254239
DOIs	https://doi.org/10.1007/978-3-031-25424-6_6
State	Published - 1 Jan 2023

Keywords

Elliptic equations
Quasiconformal mappings
Sobolev spaces

ASJC Scopus subject areas

General Mathematics
General Physics and Astronomy

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10.1007/978-3-031-25424-6_6

Cite this

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abstract = "In this article we obtain estimates of Neumann eigenvalues of p-Laplace operators in a large class of space domains satisfying quasihyperbolic boundary conditions. The suggested method is based on composition operators generated by quasiconformal mappings and their applications to Sobolev–Poincar{\'e}-inequalities. By using a sharp version of the reverse H{\"o}lder inequality we refine our estimates for quasi-balls, that is, images of balls under quasiconformal mappings of the whole space.",

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Space quasiconformal composition operators with applications to Neumann eigenvalues. / Gol’dshtein, Vladimir; Hurri-Syrjänen, Ritva; Pchelintsev, Valerii et al.
Harmonic Analysis and Partial Differential Equations: In Honor of Vladimir Maz'ya. Springer Nature, 2023. p. 141-160.

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

TY - CHAP

T1 - Space quasiconformal composition operators with applications to Neumann eigenvalues

AU - Gol’dshtein, Vladimir

AU - Hurri-Syrjänen, Ritva

AU - Pchelintsev, Valerii

AU - Ukhlov, Alexander

N1 - Publisher Copyright: © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023.

PY - 2023/1/1

Y1 - 2023/1/1

N2 - In this article we obtain estimates of Neumann eigenvalues of p-Laplace operators in a large class of space domains satisfying quasihyperbolic boundary conditions. The suggested method is based on composition operators generated by quasiconformal mappings and their applications to Sobolev–Poincaré-inequalities. By using a sharp version of the reverse Hölder inequality we refine our estimates for quasi-balls, that is, images of balls under quasiconformal mappings of the whole space.

AB - In this article we obtain estimates of Neumann eigenvalues of p-Laplace operators in a large class of space domains satisfying quasihyperbolic boundary conditions. The suggested method is based on composition operators generated by quasiconformal mappings and their applications to Sobolev–Poincaré-inequalities. By using a sharp version of the reverse Hölder inequality we refine our estimates for quasi-balls, that is, images of balls under quasiconformal mappings of the whole space.

KW - Elliptic equations

KW - Quasiconformal mappings

KW - Sobolev spaces

UR - https://www.scopus.com/pages/publications/85171502719

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EP - 160

BT - Harmonic Analysis and Partial Differential Equations

PB - Springer Nature

ER -

Space quasiconformal composition operators with applications to Neumann eigenvalues

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Keywords

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