Space quasiconformal composition operators with applications to Neumann eigenvalues

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
Article number	78
Journal	Analysis and Mathematical Physics
Volume	10
Issue number	4
DOIs	https://doi.org/10.1007/s13324-020-00420-0
Publication status	Published - Dec 2020

Keywords

Elliptic equations
Quasiconformal mappings
Sobolev spaces

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Mathematical Physics

Access to Document

10.1007/s13324-020-00420-0

Fingerprint Dive into the research topics of 'Space quasiconformal composition operators with applications to Neumann eigenvalues'. Together they form a unique fingerprint.

Cite this

@article{0ee12e3938d440e990887c63bd317a89,

title = "Space quasiconformal composition operators with applications to Neumann eigenvalues",

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.",

keywords = "Elliptic equations, Quasiconformal mappings, Sobolev spaces",

author = "Vladimir Gol{\textquoteright}dshtein and Ritva Hurri-Syrj{\"a}nen and Valerii Pchelintsev and Alexander Ukhlov",

note = "Funding Information: The first author was supported by the United States-Israel Binational Science Foundation (BSF Grant No. 2014055). The second author, whose visit to the Ben-Gurion University of Negev was supported by a grant from the Finnish Academy of Science and Letters, Vilho, Yrj{\"o} and Kalle V{\"a}is{\"a}l{\"a} Foundation, is grateful for the hospitality given by the Department of Mathematics of the Ben-Gurion University of the Negev. The third author was supported by RSF Grant No. 20-71-00037 (Results of Sect. ). Publisher Copyright: {\textcopyright} 2020, Springer Nature Switzerland AG. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",

year = "2020",

month = dec,

doi = "10.1007/s13324-020-00420-0",

language = "English",

volume = "10",

journal = "Analysis and Mathematical Physics",

issn = "1664-2368",

publisher = "Springer Science + Business Media",

number = "4",

}

TY - JOUR

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 - Funding Information: The first author was supported by the United States-Israel Binational Science Foundation (BSF Grant No. 2014055). The second author, whose visit to the Ben-Gurion University of Negev was supported by a grant from the Finnish Academy of Science and Letters, Vilho, Yrjö and Kalle Väisälä Foundation, is grateful for the hospitality given by the Department of Mathematics of the Ben-Gurion University of the Negev. The third author was supported by RSF Grant No. 20-71-00037 (Results of Sect. ). Publisher Copyright: © 2020, Springer Nature Switzerland AG. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/12

Y1 - 2020/12

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 - http://www.scopus.com/inward/record.url?scp=85095699392&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85095699392&partnerID=8YFLogxK

U2 - 10.1007/s13324-020-00420-0

DO - 10.1007/s13324-020-00420-0

M3 - Article

AN - SCOPUS:85095699392

VL - 10

JO - Analysis and Mathematical Physics

JF - Analysis and Mathematical Physics

SN - 1664-2368

IS - 4

M1 - 78

ER -