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.
Brasco, L., Mazzoleni, D. C. S., On principal frequencies, volume and inradius in convex sets, <<NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS>>, 2020; 27 (2): 1-26. [doi:10.1007/s00030-019-0614-2] [http://hdl.handle.net/10807/145703]
On principal frequencies, volume and inradius in convex sets
Mazzoleni, Dario Cesare Severo
2020
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.
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