An isoperimetric inequality for the second Robin eigenvalue of the Weighted Laplacian
Analysis of PDEs
2026-02-24 v1 Spectral Theory
Abstract
In this paper, we investigate a shape optimization problem for the second Robin eigenvalue of the weighted Laplacian on bounded Lipschitz domains symmetric about the origin. Our main theorem states that the ball centered at the origin maximizes the second Robin eigenvalue among all Lipschitz bounded domains of prescribed weighted measure and symmetric about the origin for a range of negative Robin parameters.
Keywords
Cite
@article{arxiv.2602.19456,
title = {An isoperimetric inequality for the second Robin eigenvalue of the Weighted Laplacian},
author = {Yi Gao and Kui Wang and Anqiang Zhu},
journal= {arXiv preprint arXiv:2602.19456},
year = {2026}
}
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