PreprintCC BY 4.0arXiv
Sharp Poincaré inequality for W02,p
Abstract
The first eigenvalue of the p-bilaplacian over a domain Ω is the inverse of the Poincaré constant for W02,p(Ω). In dimension two, we prove that it is minimised by disks under area constraint, thereby obtaining a sharp uniform Poincaré inequality.
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BibTeX
@misc{leylekian2026sharp,
title = {{Sharp Poincaré inequality for $W_0^2,p$}},
author = {Roméo Leylekian},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37433},
eprint = {2610.37433},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37433},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Sharp Poincaré inequality for W_0^2,p
AU - Roméo Leylekian
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37433
UR - https://arxiv.org/abs/2610.37433
AB - 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.
ER -