The Behaviour of the Eigenvalues for a Class of Operators Related to some Self-Affine Fractals in $\mathbb R^2$

W. Farkas

doi:10.4171/zaa/920

JournalszaaVol. 18, No. 4pp. 875–893

The Behaviour of the Eigenvalues for a Class of Operators Related to some Self-Affine Fractals in $R^{2}$

W. Farkas
Universität der Bundeswehr München, Neubiberg, Germany

$The Behaviour of the Eigenvalues for a Class of Operators Related to some Self-Affine Fractals in $\mathbb R^2$ cover$

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Abstract

The obtaining of sharp estimates for the asymptotic behaviour of the eigenvalues of the (semi-elliptic) operator acting in the anisotropic Sobolev space

W_{2}^{(1, 2)} (Ω) = {u \in W_{2}^{(1, 2)} (Ω) : u ∣ \partial Ω = \frac{\partial u}{\partial x _{2}} ∣ \partial Ω = 0}

generated by the quadratic form $\int_{Ω} f (γ) g (γ) d μ (γ)$ is investigated. Here $μ$ is an appropriate self-affine fractal measure on the unit disc $Ω \subset R^{2}$ .

Cite this article

W. Farkas, The Behaviour of the Eigenvalues for a Class of Operators Related to some Self-Affine Fractals in $R^{2}$ . Z. Anal. Anwend. 18 (1999), no. 4, pp. 875–893

DOI 10.4171/ZAA/920