On principal frequencies and inradius in convex sets

We generalize to the case of the p-Laplacian an old result by Hersch and Protter. Namely, we show that it is possible to estimate from below the first eigenvalue of the Dirichlet p-Laplacian of a convex set in terms of its inradius. We also prove a lower bound in terms of isoperimetric ratios and we...

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Main Author:	Lorenzo Brasco
Format:	Article
Language:	English
Published:	University of Bologna 2018-12-01
Series:	Bruno Pini Mathematical Analysis Seminar
Subjects:	convex sets p-laplacian nonlinear eigenvalue problems inradius cheeger constant
Online Access:	https://mathematicalanalysis.unibo.it/article/view/8945

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spelling	doaj-1e0021bca0eb4ca898d3a5c15cd9754a2020-11-25T00:49:48ZengUniversity of BolognaBruno Pini Mathematical Analysis Seminar2240-28292018-12-01917810110.6092/issn.2240-2829/89457786On principal frequencies and inradius in convex setsLorenzo Brasco0Università degli Studi di FerraraWe generalize to the case of the p-Laplacian an old result by Hersch and Protter. Namely, we show that it is possible to estimate from below the first eigenvalue of the Dirichlet p-Laplacian of a convex set in terms of its inradius. We also prove a lower bound in terms of isoperimetric ratios and we briefly discuss the more general case of Poincarè-Sobolev embedding constants. Eventually, we highlight an open problem.https://mathematicalanalysis.unibo.it/article/view/8945convex setsp-laplaciannonlinear eigenvalue problemsinradiuscheeger constant
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Lorenzo Brasco
spellingShingle	Lorenzo Brasco On principal frequencies and inradius in convex sets Bruno Pini Mathematical Analysis Seminar convex sets p-laplacian nonlinear eigenvalue problems inradius cheeger constant
author_facet	Lorenzo Brasco
author_sort	Lorenzo Brasco
title	On principal frequencies and inradius in convex sets
title_short	On principal frequencies and inradius in convex sets
title_full	On principal frequencies and inradius in convex sets
title_fullStr	On principal frequencies and inradius in convex sets
title_full_unstemmed	On principal frequencies and inradius in convex sets
title_sort	on principal frequencies and inradius in convex sets
publisher	University of Bologna
series	Bruno Pini Mathematical Analysis Seminar
issn	2240-2829
publishDate	2018-12-01
description	We generalize to the case of the p-Laplacian an old result by Hersch and Protter. Namely, we show that it is possible to estimate from below the first eigenvalue of the Dirichlet p-Laplacian of a convex set in terms of its inradius. We also prove a lower bound in terms of isoperimetric ratios and we briefly discuss the more general case of Poincarè-Sobolev embedding constants. Eventually, we highlight an open problem.
topic	convex sets p-laplacian nonlinear eigenvalue problems inradius cheeger constant
url	https://mathematicalanalysis.unibo.it/article/view/8945
work_keys_str_mv	AT lorenzobrasco onprincipalfrequenciesandinradiusinconvexsets
_version_	1725251125411577856

On principal frequencies and inradius in convex sets

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