Calculus of Variations and Geometric Measure Theory

L. Brasco - D. Mazzoleni

On principal frequencies, volume and inradius in convex sets

created by brasco on 19 Nov 2019
modified by mazzoleni on 08 Jan 2020


Accepted Paper

Inserted: 19 nov 2019
Last Updated: 8 jan 2020

Journal: NoDEA
Year: 2019


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