Zeitschrift für Analysis und ihre Anwendungen Vol. 18, No. 4, pp. 875893 (1999) 

The Behaviour of the Eigenvalues for a Class of Operators Related to some SelfAffine Fractals in $R^2$W. FarkasUniv. Bundeswehr München, Inst. Theor. Inf. & Math., WernerHeisenbergWeg 39, D85577 NeubibergAbstract: The obtaining of sharp estimates for the asymptotic behaviour of the eigenvalues of the (semielliptic) operator acting in the anisotropic Sobolev space $$ Ø{W}_2^{(1,2)}(\Omega) = \left\{u \in W^{(1,2)}_2(\Omega): \, u\partial \Omega = {\partial u \over \partial x_2} \, \partial\Omega = 0\right\} $$ generated by the quadratic form $\int_\Omega f(\gamma )\,\overline{g(\gamma)} \,d\mu(\gamma)$ is investigated. Here $\mu$ is an appropriate selfaffine fractal measure on the unit disc $\Omega \subset \R^2$. Keywords: regular anisotropic fractals, anisotropic function spaces, semielliptic differential operators Classification (MSC2000): 35P15, 46E35, 28A90 Full text of the article:
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