Green's functions on fractals (Q2709708)

Finitely ramified self-similar fractals possessing a ``Laplacian'' in the sense of Kigami are considered. Several recursive formulae are given to calculate the Green's function \(G\) with Dirichlet boundary condition in \(V_0\). They are used to describe the decay of \(G\) at the boundary and its global maximum. A local Green's function \(G_z\) with vanishing zero and first order data at the point \(z\in V_0\) was introduced by \textit{R. S. Strichartz} [J. Funct. Anal. 174, 76-127 (2000; Zbl 0956.31007)]. Theorem~4.2 gives a singular integral representation of solutions to the Poisson equation with zero and first order vanishing boundary conditions at \(z\).