On principal frequencies, volume and inradius in convex sets
Spectral Theory
2020-01-01 v2 Analysis of PDEs
Abstract
We provide a sharp double-sided estimate for Poincar\'e-Sobolev constants on a convex set, in terms of its inradius and 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
Cite
@article{arxiv.1911.08256,
title = {On principal frequencies, volume and inradius in convex sets},
author = {Lorenzo Brasco and Dario Mazzoleni},
journal= {arXiv preprint arXiv:1911.08256},
year = {2020}
}
Comments
23 pages, 3 figures