Calculus of Variations and Geometric Measure Theory
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L. Brasco - D. Mazzoleni

On principal frequencies, volume and inradius in convex sets

created by brasco on 19 Nov 2019

[BibTeX]

Preprint

Inserted: 19 nov 2019
Last Updated: 19 nov 2019

Pages: 22
Year: 2019

Abstract:

We provide a sharp double-sided estimate for Poincar\'e-Sobolev constants on a convex set, in terms of its inradius and $N-$dimensional measure. Our results extend and unify previous works by Hersch and Protter (for the first eigenvalue) and of Makai, P\'olya and Szeg\H{o} (for the torsional rigidity), by means of a single proof.

Keywords: Nonlinear eigenvalue problems, convex sets, Torsional rigidity, Inradius


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