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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