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.
|Numero di pagine
|NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS
|Stato di pubblicazione
|Pubblicato - 2020
- Convex sets
- Nonlinear eigenvalue problems
- Torsional rigidity