Spectral estimates of the p-Laplace Neumann operator in conformal regular domains

In this paper we study spectral estimates of the p-Laplace Neumann operator in conformal regular domains Ω⊂R2. This study is based on (weighted) Poincaré–Sobolev inequalities. The main technical tool is the theory of composition operators in relation with the Brennan’s conjecture. We prove that if t...

Full description

Saved in:
Bibliographic Details
Published in:Transactions of A. Razmadze Mathematical Institute 2016-05, Vol.170 (1), p.137-148
Main Authors: Gol’dshtein, V., Ukhlov, A.
Format: Article
Language:English
Subjects:
Conformal mappings
Elliptic equations
Sobolev spaces
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper we study spectral estimates of the p-Laplace Neumann operator in conformal regular domains Ω⊂R2. This study is based on (weighted) Poincaré–Sobolev inequalities. The main technical tool is the theory of composition operators in relation with the Brennan’s conjecture. We prove that if the Brennan’s conjecture holds for any p∈(4/3,2) and r∈(1,p/(2−p)) then the weighted (r,p)-Poincare–Sobolev inequality holds with the constant depending on the conformal geometry of Ω. As a consequence we obtain classical Poincare–Sobolev inequalities and spectral estimates for the first nontrivial eigenvalue of the p-Laplace Neumann operator for conformal regular domains.
ISSN:2346-8092
DOI:10.1016/j.trmi.2016.03.002