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 originale | English |
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pagine (da-a) | 1-26 |
Numero di pagine | 26 |
Rivista | NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS |
Volume | 27 |
DOI | |
Stato di pubblicazione | Pubblicato - 2020 |
Keywords
- Convex sets
- Inradius
- Nonlinear eigenvalue problems
- Torsional rigidity