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The Distribution of Eigenfrequencies of Anisotropic Fractal Drums
Author(s) -
Farkas Walter,
Triebel Hans
Publication year - 1999
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s002461079900770x
Subject(s) - fractal , laplace operator , mathematics , mathematical analysis , sobolev space , bounded function , distribution (mathematics) , eigenvalues and eigenvectors , dirichlet distribution , trace operator , anisotropy , multifractal system , fractal derivative , operator (biology) , domain (mathematical analysis) , differential operator , geometry , pure mathematics , physics , boundary (topology) , fractal dimension , boundary value problem , fractal analysis , elliptic boundary value problem , quantum mechanics , biochemistry , chemistry , repressor , transcription factor , gene , free boundary problem
Let Γ be an anisotropic fractal. The aim of the paper is to investigate the distribution of the eigenvalues of the fractal differential operator (−Δ) −1 o tr Γ acting in the classical Sobolev spaceW ^ 2 1 ( Ω )where Ω is a bounded C ∞ domain in the plane R 2 with Γ⊂Ω. Here −Δ is the Dirichlet Laplacian in Ω and tr Γ is closely related to the trace operator tr Γ .