Several isoperimetric inequalities of Dirichlet and Neumann eigenvalues of the Witten-Laplacian

2024/03/12 by Ruifeng Chen, Jing Mao, Chen, Ruifeng +1 · 1 citation
Materials Science · Mathematics · #35J10 #35J15 #35P15 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Graph theory and applications #Quasicrystal Structures and Properties #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2403.08075

openalex publication_date 2024/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, by mainly using the rearrangement technique and suitably constructing trial functions, under the constraint of fixed weighted volume, we can successfully obtain several isoperimetric inequalities for the first and the second Dirichlet eigenvalues, the first nonzero Neumann eigenvalue of the Witten-Laplacian on bounded domains in space forms. These spectral isoperimetric inequalities extend those classical ones (i.e. the Faber-Krahn inequality, the Hong-Krahn-Szegő inequality and the Szegő-Weinberger inequality) of the Laplacian.

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• Spectral isoperimetric inequalities for a class of mixed eigenvalue problems of the Laplacian on triangles and trapezoids

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