PreprintCC BY-SA 4.0arXiv
On Faber-Krahn inequality for Dirichlet Fractional-Logarithmic Laplacian
Abstract
We study the Faber--Krahn problem for the fractional--logarithmic Laplacian (−Δ)s+ln, 0<s<1, with Fourier symbol |ξ|2sln|ξ|2. We prove a small-volume and large-volume dichotomy. For sufficiently small volume, balls minimize the first Dirichlet eigenvalue, with rigidity up to translation.
Related
- Faber-Krahn inequality for the first Dirichlet eigenvalues of the logarithmic Hardy operator
- Faber--Krahn inequality for homogeneous normalized p-Laplacian type operators
- The fractional Faber--Krahn inequality in sharp quantitative form
- Explicit sharp gradient stability of the Lp-Poincaré inequality and fundamental gaps for the Dirichlet p-Laplacian operator
- Optimal Hardy weights for the fractional discrete Dirichlet Laplacian on the half-line
BibTeX
@misc{chen2026faberkrahn,
title = {{On Faber-Krahn inequality for Dirichlet Fractional-Logarithmic Laplacian}},
author = {Huyuan Chen and Rui Chen and Bobo Hua},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15481},
eprint = {2609.15481},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15481},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - On Faber-Krahn inequality for Dirichlet Fractional-Logarithmic Laplacian
AU - Huyuan Chen
AU - Rui Chen
AU - Bobo Hua
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.15481
UR - https://arxiv.org/abs/2609.15481
AB - We study the Faber--Krahn problem for the fractional--logarithmic Laplacian (−Δ)^s+ln, 0<s<1, with Fourier symbol |ξ|^2sln|ξ|^2. We prove a small-volume and large-volume dichotomy. For sufficiently small volume, balls minimize the first Dirichlet eigenvalue, with rigidity up to translation.
ER -