Payne–Polya–Weinberger, Hile–Protter and Yang’s Inequalities for Dirichlet Laplace Eigenvalues on Integer Lattices

Payne–Polya–Weinberger, Hile–Protter and Yang’s Inequalities for Dirichlet Laplace Eigenvalues on Integer Lattices

In this paper, we prove some analogues of Payne–Polya–Weinberger, Hile–Protter and Yang’s inequalities for Dirichlet (discrete) Laplace eigenvalues on any subset in the integer lattice Z n . This partially answers a question posed by Chung and Oden (Pac J Math 192(2):257–273, 2000).

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Veröffentlicht in:The Journal of Geometric Analysis 2023-07, Vol.33 (7), Article 217
Hauptverfasser: Hua, Bobo, Lin, Yong, Su, Yanhui
Format: Artikel
Sprache:eng
Schlagworte:
Abstract Harmonic Analysis
Convex and Discrete Geometry
Differential Geometry
Dirichlet problem
Dynamical Systems and Ergodic Theory
Eigenvalues
Fourier Analysis
Geometry
Global Analysis and Analysis on Manifolds
Inequalities
Integers
Lattices
Mathematics
Mathematics and Statistics
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Zusammenfassung:In this paper, we prove some analogues of Payne–Polya–Weinberger, Hile–Protter and Yang’s inequalities for Dirichlet (discrete) Laplace eigenvalues on any subset in the integer lattice Z n . This partially answers a question posed by Chung and Oden (Pac J Math 192(2):257–273, 2000).
ISSN:1050-6926
1559-002X
DOI:10.1007/s12220-023-01284-z