A characterization for elliptic problems on fractal sets

In this paper we prove a characterization theorem on the existence of one non-zero strong solution for elliptic equations defined on the Sierpinski gasket. More generally, the validity of our result can be checked studying elliptic equations defined on self-similar fractal domains whose spectral dimension nu is an element of (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