On the Pólya conjecture and the weak Weyl-Berry conjecture

DOI10.1007/BF02829904zbMath0921.35119OpenAlexW2008756163WikidataQ123245193 ScholiaQ123245193MaRDI QIDQ4234443

Hua Chen, Sleeman, Brian D.

Publication date: 29 September 1999

Published in: Wuhan University Journal of Natural Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02829904

zbMATH Keywords

fractal domainDirichlet counting functionNeumann counting functionWeyl term

Mathematics Subject Classification ID

Asymptotic distributions of eigenvalues in context of PDEs (35P20) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Cites Work

• Can one hear the dimension of a fractal?
• Fractal drums and the \(n\)-dimensional modified Weyl-Berry conjecture
• On the Eigenvalues of Vibrating Membranes^†
• Fractal Drum, Inverse Spectral Problems for Elliptic Operators and a Partial Resolution of the Weyl-Berry Conjecture
• Counting function asymptotics and the weak Weyl-Berry conjecture for connected domains with fractal boundaries
• An Example of a Two-Term Asymptotics for the "Counting Function" of a Fractal Drum
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