Accepted Paper
Inserted: 19 nov 2019
Last Updated: 8 jan 2020
Journal: NoDEA
Year: 2019
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.
Keywords: Nonlinear eigenvalue problems, convex sets, Torsional rigidity, Inradius
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