Spectra of Laplacians on Fractal Domains

Michel Lapidus
University of California, Riverside (UC Riverside)

We plan to give a survey of some results concerning the eigenvalues and eigenfunctions of Laplacians (and other differential operators, with suitable boundary conditions) on domains with fractal boundaries. In particular, we will address aspects of the question “Can one hear the shape of a fractal drum?” If time permits, we will also briefly discuss the case when the “domain” itself is fractal. These theoretical and numerical or computer graphics-aided results are relevant to the long-term problem of understanding the origin of fractality in nature.

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