PreprintCC BY 4.0arXiv
The Faber-Krahn inequality for p-Hermite operators
Abstract
We prove a Faber-Krahn inequality for the first eigenvalue of the p-Hermite operator (the weighted p-Laplacian with Gaussian weight) on Lipschitz domains in Rn under Robin boundary conditions with positive Robin parameter. The main result states that, among all domains of given Gaussian measure, the first eigenvalue is minimized by a half-space, and equality holds only for half-spaces. This extends the classical Faber-Krahn inequalities for the p-Laplacian \cite{BucurCV} to the p-Hermite operator and generalizes the linear case \cite{ChiacchioMathann} to the full nonlinear regime p>1.
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BibTeX
@misc{sun2026faberkrahn,
title = {{The Faber-Krahn inequality for $p$-Hermite operators}},
author = {Xiaomei Sun and Kui Wang and Anqiang Zhu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01269},
eprint = {2609.01269},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01269},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Faber-Krahn inequality for p-Hermite operators
AU - Xiaomei Sun
AU - Kui Wang
AU - Anqiang Zhu
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.01269
UR - https://arxiv.org/abs/2609.01269
AB - We prove a Faber-Krahn inequality for the first eigenvalue of the p-Hermite operator (the weighted p-Laplacian with Gaussian weight) on Lipschitz domains in R^n under Robin boundary conditions with positive Robin parameter. The main result states that, among all domains of given Gaussian measure, the first eigenvalue is minimized by a half-space, and equality holds only for half-spaces. This extends the classical Faber-Krahn inequalities for the p-Laplacian \cite{BucurCV} to the p-Hermite operator and generalizes the linear case \cite{ChiacchioMathann} to the full nonlinear regime p>1.
ER -