On the eigenfunctions and the first eigenvalue of fractal drums

by    H. Triebel

Preprint series: 99-14, Analysis

46E35 Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
35P20 Asymptotic distribution of eigenvalues and eigenfunctions for PDO
28A80 Fractals, See also {58Fxx}

Abstract: The paper deals with the smoothness of eigenfunctions and the simplicity of the first eigenvalue of $B = ( - \Delta )^{- 1} \circ \mu$, where $-\Delta$ is the Dirichlet Laplacian in a bounded $C^\infty$ domain in ${\Bbb{R}}^n$ and $\mu$ is a fractal measure.

Upload: 1999-03-03

Update: 1999-03-03

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