We provide a sharp double-sided estimate for Poincaré–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, Pólya and Szegő (for the torsional rigidity), by means of a single proof.

On principal frequencies, volume and inradius in convex sets

Mazzoleni D.
2020-01-01

Abstract

We provide a sharp double-sided estimate for Poincaré–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, Pólya and Szegő (for the torsional rigidity), by means of a single proof.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11571/1331746
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 8
  • ???jsp.display-item.citation.isi??? 7
social impact