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

Loading next page...
 
/lp/springer_journal/spectral-estimates-of-the-p-laplace-neumann-operator-and-brennan-s-IOym7USbjo
Publisher
Springer International Publishing
Copyright
Copyright © 2017 by Unione Matematica Italiana
Subject
Mathematics; Mathematics, general
ISSN
1972-6724
eISSN
2198-2759
D.O.I.
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 ItalianaSpringer Journals

Published: May 17, 2017

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off