A characterization for elliptic problems on fractal sets
Giovanni Molica Bisci, Vicenţiu D. Rădulescu · Proceedings of the American Mathematical Society · 2015
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 ν ∈ ( 0 , 2 ) u \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.