Year: 2025
Type: article
Abstract: We prove a two-sided estimate on the sharp Lp Poincaré constant of a general open set, in terms of a capacitary variant of its inradius. This extends a result by Maz’ya and Shubin, originally devised for the case p = 2, in the subconformal regime. We cover the whole range of p, by allowing in particular the extremal cases p = 1 (Cheeger’s constant) and p = N (conformal case), as well. We also discuss the more general case of the sharp Poincaré-Sobolev embedding constants and get an analogous result. Finally, we present a brief discussion on the superconformal case, as well as some examples and counter-examples.
Authors: Francesco Bozzola, Lorenzo Brasco
Institutions: University of Parma, University of Ferrara
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G6214568023
OpenAlex ID: W7110917825
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