Fractal drums and the \(n\)-dimensional modified Weyl-Berry conjecture

DOI10.1007/BF02101845zbMath0841.35075OpenAlexW1971147515WikidataQ114018446 ScholiaQ114018446MaRDI QIDQ1894847

Hua Chen, Sleeman, Brian D.

Publication date: 22 August 1995

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02101845

zbMATH Keywords

counting functionDirichlet LaplacianMinkowski dimensionfractal boundaryexplicit upper and lower boundssecond termtessellation of domains

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Variational methods for second-order elliptic equations (35J20)

Related Items (7)

On spectral asymptotics for domains with fractal boundaries ⋮ Fractal drums and the \(n\)-dimensional modified Weyl-Berry conjecture ⋮ Computing eigenvalues of the Laplacian on rough domains ⋮ Inverse problems for a general multi-connected bounded drum with applications in physics. ⋮ Well-Posed PDE and Integral Equation Formulations for Scattering by Fractal Screens ⋮ Counting function asymptotics and the weak Weyl-Berry conjecture for connected domains with fractal boundaries ⋮ On the Pólya conjecture and the weak Weyl-Berry conjecture

Cites Work

• Can one hear the dimension of a fractal?
• Second term of the spectral asymptotic expansion of the Laplace-Beltrami operator on manifolds with boundary
• A sharp asymptotic remainder estimate for the eigenvalues of the Laplacian in a domain of \(R^3\)
• Fractal drums and the \(n\)-dimensional modified Weyl-Berry conjecture
• One-dimensional cohomologies of discrete subgroups
• An Estimate Near the Boundary for the Spectral Function of the Laplace Operator
• Fractal Drum, Inverse Spectral Problems for Elliptic Operators and a Partial Resolution of the Weyl-Berry Conjecture
• An Example of a Two-Term Asymptotics for the "Counting Function" of a Fractal Drum
• Can One Hear the Shape of a Drum?
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