加权Laplace算子Dirichlet特征值问题的一个万有不等式及其应用

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Yang Guicheng, Wen Yangzhe, Mao Jing. A Universal Inequality for the Dirichlet Eigenvalue Problem of the Weighted Laplacian and its Application[J].Acta mathematica scientia,Series A, 2025, 45(1): 54-73.

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References 20

[1]	Ashbaugh M S, Benguria R D. Bounds for ratios of the first, second, and third membrane eigenvalues// Angell T, Pamela Cook L, Kleinman R, Olmstead W. Nonlinear Problems in Applied Mathematics. Philadelphia: Soc Indu Appl Math, 1996: 30-42
[2]	Ashbaugh M S, Benguria R D. The range of values of $\frac{{{\lambda _2}}}{{{\lambda _1}}}$ and $\frac{{{\lambda _3}}}{{{\lambda _1}}}$ for the fixed membrane problem. Reviews in Mathematical Physics, 1994, 6(5a): 999-1009
[3]	Faber G. Beweis, dass unter allen homogenen Membranen von gleicher Fläche und gleicher Spannung die kreisförmige den tiefsten Grundton gibt// München Z. Sitzungsber Bayer Akad Wiss München Math-Phys KI, 1923: 169-172
[4]	Brands J. Bounds for the ratios of the first three membrane eigenvalues. Archive for Rational Mechanics and Analysis, 1964, 16: 265-268
[5]	Chavel I. Eigenvalues in Riemannian Geometry. Orlando: Academic Press, 1984
[6]	Chen D G, Zheng T. Bounds for ratios of the membrane eigenvalues. Journal of Differential Equations, 2011, 250(3): 1575-1590
[7]	Cheng Q M. Universal estimates for eigenvalues and applications// Proceedings of the 6th International Congress of Chinese Mathematicians. Advanced Lectures in Mathematics, 2016: 37-52
[8]	Cheng Q M, Qi X. Inequalities for eigenvalues of the Laplacian. arXiv:1104.5298v1
[9]	Cheng Q M, Yang H. Bounds on eigenvalues of Dirichlet Laplacian. Mathematische Annalen, 2007, 337(1): 159-175
[10]	Hile G N, Protter M H. Inequalities for eigenvalues of the Laplacian. Indiana University Mathematics Journal, 1980, 29(4): 523-538
[11]	Krahn E. Über eine von Rayleigh formulierte Minimaleigenschaft des Kreises. Mathematische Annalen, 1925, 94(1): 97-100
[12]	Levitin M, Parnovski L. Commutators spectral trace identities, and universal estimates for eigenvalues. J Funct Anal, 2002, 192(2): 425-445
[13]	Lu W, Mao J, Wu C X, Zeng L Z. Eigenvalue estimates for the drifting Laplacian and the $p$ -Laplacian on submanifolds of warped products. Applicable Analysis, 2021, 100(11): 2275-2300
[14]	Payne L E, Pólya G, Weinberger H F. On the ratio of consecutive eigenvalues. Journal of Mathematical Physics, 1956, 35(1-4): 289-298
[15]	Pólya G. On the eigenvalues of vibrating membranes. Proceedings of the London Mathematical Society, 1961, 11(3): 419-433
[16]	Rosales C, Canete A, Bayle V, Morgan F. On the isoperimetric problem in Euclidean space with density. Calculus of Variations and Partial Differential Equations, 2008, 31(1): 27-46
[17]	Thompson C J. On the ratio of consecutive eigenvalues in $n$ -dimensions. Studies in Applied Mathematics, 1969, 48(3): 281-283
[18]	Wei G F, Wylie W. Comparison geometry for the Bakry-Émery Ricci tensor. Journal of Differential Geometry, 2009, 83(2): 337-405
[19]	Yang H C. An estimate of the difference between consecutive eigenvalues. International Centre for Theoretical Physics, 1991
[20]	Zeng L Z, Sun H J. Eigenvalues of the drifting Laplacian on smooth metric measure spaces. Pacific J Math, 2022, 319(2): 439-470

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A Universal Inequality for the Dirichlet Eigenvalue Problem of the Weighted Laplacian and its Application

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