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Mathematics > Analysis of PDEs
Title: Several isoperimetric inequalities of Dirichlet and Neumann eigenvalues of the Witten-Laplacian
(Submitted on 12 Mar 2024 (v1), last revised 27 Mar 2024 (this version, v2))
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-Szeg\H{o} inequality and the Szeg\H{o}-Weinberger inequality) of the Laplacian.
Submission history
From: Mao Jing [view email][v1] Tue, 12 Mar 2024 20:58:51 GMT (25kb)
[v2] Wed, 27 Mar 2024 14:34:52 GMT (26kb)
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