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THE DISTRIBUTION OF EIGENFREQUENCIES OF ANISOTROPIC FRACTAL DRUMS

Published online by Cambridge University Press:  01 August 1999

WALTER FARKAS  and
HANS TRIEBEL
WALTER FARKAS
Affiliation:
Bucharest University, Faculty of Mathematics, 14. Academiei Str., RO-70109 Bucharest, Romania Current address: Institut für Theoretische Informatik und Mathematik, Universität der Bundeswehr, Werner-Heisenberg-Weg 39, D-85 577 Neubiberg, Germany.
HANS TRIEBEL
Affiliation:
Friedrich Schiller Universität Jena, Mathematisches Institut, Ernst-Abbe-Platz 1–4, D-07740 Jena, Germany
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Abstract

Let Γ be an anisotropic fractal. The aim of the paper is to investigate the distribution of the eigenvalues of the fractal differential operator

formula here

acting in the classical Sobolev space W˚12(Ω) where Ω is a bounded C∞ domain in the plane ℝ2 with Γ⊂Ω. Here −Δ is the Dirichlet Laplacian in Ω and trΓ is closely related to the trace operator trΓ.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 60 , Issue 1 , August 1999 , pp. 224 - 236
Copyright
The London Mathematical Society 1999

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