May 30, 2024Open Access

Stability of the second non trivial eigenvalue of the Neumann Laplacian

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Abstract

In this paper, building on the ideas of Brasco and Pratelli (Geom. Funct. Anal., 22 (2012), 107-135), we establish a stability estimate for Bucur and Henrot's inequality (Acta Math., 222 (2019), 337-361). Their inequality asserts that, among regular sets of given measure, the disjoint union of two balls with the same radius maximizes the second non trivial eigenvalue of the Neumann Laplacian.

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Xin Liao (Thu,) studied this question.

synapsesocial.com/papers/68e67cafb6db64358760604f https://doi.org/https://doi.org/10.48550/arxiv.2405.20050

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