A characterization for elliptic problems on fractal sets

Molica Bisci, Giovanni; Rădulescu, Vicenţiu

doi:10.1090/S0002-9939-2015-12475-6

A characterization for elliptic problems on fractal sets
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by Giovanni Molica Bisci and Vicenţiu D. Rădulescu

Proc. Amer. Math. Soc. 143 (2015), 2959-2968

DOI: https://doi.org/10.1090/S0002-9939-2015-12475-6

Published electronically: February 13, 2015

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Abstract:

In this paper we prove a characterization theorem on the existence of one non-zero strong solution for elliptic equations defined on the Sierpiński gasket. More generally, the validity of our result can be checked studying elliptic equations defined on self-similar fractal domains whose spectral dimension $\nu \in (0,2)$. Our theorem can be viewed as an elliptic version on fractal domains of a recent contribution obtained in a recent work of Ricceri for a two-point boundary value problem.

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