On principal frequencies, volume and inradius in convex sets

Lorenzo Brasco; Dario Mazzoleni

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arXiv · 1911.08256

On principal frequencies, volume and inradius in convex sets

Lorenzo Brasco·Dario Mazzoleni

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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.

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Lorenzo Brasco, Dario Mazzoleni. 2019-11-19. On principal frequencies, volume and inradius in convex sets. https://arxiv.org/abs/1911.08256

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