On the Mountain Pass Solutions to Boundary Value Problems on the Sierpinski Gasket

Boundary Value Problems on a Half Sierpinski Gasket

We study boundary value problems for the Laplacian on a domain Ω consisting of the left half of the Sierpinski Gasket (SG), whose boundary is essentially a countable set of points X. For harmonic functions we give an explicit Poisson integral formula to recover the function from its boundary values, and characterize those that correspond to functions of finite energy. We give an explicit Dirich...

A note on elliptic problems on the Sierpinski gasket

Using a method that goes back to J. Saint Raymond, we prove the existence of infinitely many weak solutions of certain nonlinear elliptic problems defined on the SG. Mathematics Subject Classification (2010): 35J20, 28A80, 35J25, 35J60, 47J30, 49J52.

Sampling on the Sierpinski Gasket

Random walks on the Sierpinski Gasket

The generating functions for random walks on the Sierpinski gasket are computed. For closed walks, we investigate the dependence of these functions on location and the bare hopping parameter. They are continuous on the infinite gasket but not differentiable. J. Physique 47 (1986) 1663-1669 OCTOBRE 1986, Classification Physics Abstracts 05.40 05.50 1. Preliminaries and review of known results. C...

Spanning Forests on the Sierpinski Gasket

We present the numbers of spanning forests on the Sierpinski gasket SGd(n) at stage n with dimension d equal to two, three and four, and determine the asymptotic behaviors. The corresponding results on the generalized Sierpinski gasket SGd,b(n) with d = 2 and b = 3, 4 are obtained. We also derive the upper bounds of the asymptotic growth constants for both SGd and SG2,b.