Sharp Poincaré inequality for $W_0^{2,p}$

The first eigenvalue of the $p$-bilaplacian over a domain $Ω$ is the inverse of the Poincaré constant for $W_0^{2,p}(Ω)$. In dimension two, we prove that it is minimised by disks under area constraint, thereby obtaining a sharp uniform Poincaré inequality.

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-10-27
DOI
https://doi.org/10.48550/arxiv.2610.37433
Primary Topic
Nonlinear Partial Differential Equations
Type
preprint
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preprint

Sharp Poincaré inequality for $W_0^{2,p}$

Roméo Leylekian
arXiv (Cornell University)
Nonlinear Partial Differential Equations
preprint

Sharp Poincaré inequality for $W_0^{2,p}$

Roméo Leylekian
preprint en

Abstract

The first eigenvalue of the $p$-bilaplacian over a domain $Ω$ is the inverse of the Poincaré constant for $W_0^{2,p}(Ω)$. In dimension two, we prove that it is minimised by disks under area constraint, thereby obtaining a sharp uniform Poincaré inequality.

arXiv (Cornell University)
Nonlinear Partial Differential Equations
DOIOpen Access PDFOpenAlex
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Sharp Poincaré inequality for $W_0^{2,p}$ — Roméo Leylekian · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS