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Mathematics > Analysis of PDEs
Title: On the Ashbaugh-Benguria type conjecture about lower-order Neumann eigenvalues of the Witten-Laplacian
(Submitted on 12 Mar 2024 (v1), last revised 27 Mar 2024 (this version, v2))
Abstract: An isoperimetric inequality for lower order nonzero Neumann eigenvalues of the Witten-Laplacian on bounded domains in a Euclidean space or a hyperbolic space has been proven in this paper. About this conclusion, we would like to point out two things:
It strengthens the well-known Szeg\H{o}-Weinberger inequality for nonzero Neumann eigenvalues of the classical free membrane problem given in [J. Rational Mech. Anal. 3 (1954) 343-356] and [J. Rational Mech. Anal. 5 (1956) 633-636];
Recently, Xia-Wang [Math. Ann. 385 (2023) 863-879] gave a very important progress to the celebrated conjecture of M. S. Ashbaugh and R. D. Benguria proposed in [SIAM J. Math. Anal. 24 (1993) 557-570]. It is easy to see that our conclusion here covers Xia-Wang's this progress as a special case.
In this paper, we have also proposed two open problems which can be seen as a generalization of Ashbaugh-Benguria's conjecture mentioned above.
Submission history
From: Mao Jing [view email][v1] Tue, 12 Mar 2024 20:45:10 GMT (16kb)
[v2] Wed, 27 Mar 2024 05:33:42 GMT (16kb)
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