On principal frequencies, volume and inradius in convex sets

Dario Cesare Severo Mazzoleni, Lorenzo Brasco

Risultato della ricerca: Contributo in rivistaArticolo in rivistapeer review

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.
Lingua originaleEnglish
pagine (da-a)1-26
Numero di pagine26
RivistaNODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS
Volume27
DOI
Stato di pubblicazionePubblicato - 2020

Keywords

  • Convex sets
  • Inradius
  • Nonlinear eigenvalue problems
  • Torsional rigidity

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