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arXiv · 2602.19456

An isoperimetric inequality for the second Robin eigenvalue of the Weighted Laplacian

Yi Gao·Kui Wang·Anqiang Zhu
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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.

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Yi Gao, Kui Wang, Anqiang Zhu. 2026-02-23. An isoperimetric inequality for the second Robin eigenvalue of the Weighted Laplacian. https://arxiv.org/abs/2602.19456

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