Boundary value problems on part of a level-n Sierpinski gasket

Abstract

Abstract We study the boundary value problems for the Laplacian on a sequence of domains constructed by cutting level-n Sierpinski gaskets properly. Under proper assumptions on these domains, we manage to give an explicit Poisson integral formula to obtain a series of solutions subject to the boundary data. In particular, it is proved that there exists a unique solution continuous on the closure of the domain for a given sequence of convergent boundary values.

Keywords

• boundary value problems
• level-n Sierpinski gasket
• harmonic functions
• postcritically finite
• fractal Laplacian