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

Vladimir Gol’dshtein, Valerii Pchelintsev, Alexander Ukhlov

Research output: Contribution to journalArticle

2 Citations (Scopus)

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 languageEnglish
Pages (from-to)245-264
Number of pages20
JournalBolletino dell Unione Matematica Italiana
Volume11
Issue number2
DOIs
Publication statusPublished - 1 Jun 2018

Fingerprint

Quasiconformal
Laplace
Quasiconformal Mapping
Composition Operator
Operator
Estimate
Eigenvalue

Keywords

  • Elliptic equations
  • Quasiconformal mappings
  • Sobolev spaces

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Spectral estimates of the p-Laplace Neumann operator and Brennan’s conjecture. / Gol’dshtein, Vladimir; Pchelintsev, Valerii; Ukhlov, Alexander.

In: Bolletino dell Unione Matematica Italiana, Vol. 11, No. 2, 01.06.2018, p. 245-264.

Research output: Contribution to journalArticle

@article{0ea9bd3dc5e14cc5b156972e23b6d6cf,
title = "Spectral estimates of the p-Laplace Neumann operator and Brennan’s conjecture",
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’s conjecture for (quasi)conformal mappings.",
keywords = "Elliptic equations, Quasiconformal mappings, Sobolev spaces",
author = "Vladimir Gol’dshtein and Valerii Pchelintsev and Alexander Ukhlov",
year = "2018",
month = "6",
day = "1",
doi = "10.1007/s40574-017-0127-z",
language = "English",
volume = "11",
pages = "245--264",
journal = "Bolletino dell Unione Matematica Italiana",
issn = "1972-6724",
publisher = "Unione Matematica Italiana",
number = "2",

}

TY - JOUR

T1 - Spectral estimates of the p-Laplace Neumann operator and Brennan’s conjecture

AU - Gol’dshtein, Vladimir

AU - Pchelintsev, Valerii

AU - Ukhlov, Alexander

PY - 2018/6/1

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

UR - http://www.scopus.com/inward/record.url?scp=85035766902&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85035766902&partnerID=8YFLogxK

U2 - 10.1007/s40574-017-0127-z

DO - 10.1007/s40574-017-0127-z

M3 - Article

VL - 11

SP - 245

EP - 264

JO - Bolletino dell Unione Matematica Italiana

JF - Bolletino dell Unione Matematica Italiana

SN - 1972-6724

IS - 2

ER -