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

Spectral estimates of the p-Laplace Neumann operator and Brennan’s conjecture 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 $$\varOmega \subset {\mathbb {R}}^2$$ Ω ⊂ R 2 . 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 $$\alpha $$ 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bollettino dell'Unione Matematica Italiana Springer Journals

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

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Publisher
Springer Journals
Copyright
Copyright © 2017 by Unione Matematica Italiana
Subject
Mathematics; Mathematics, general
ISSN
1972-6724
eISSN
2198-2759
DOI
10.1007/s40574-017-0127-z
Publisher site
See Article on Publisher Site

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 $$\varOmega \subset {\mathbb {R}}^2$$ Ω ⊂ R 2 . 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 $$\alpha $$ 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.

Journal

Bollettino dell'Unione Matematica Italiana – Springer Journals

Published: May 17, 2017

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