The p-Laplacian on the Sierpinski gasket

We define a nonlinear p-Laplacian operator, Delta(p), on the Sierpinski gasket, for 1 < p < infinity, generalizing the linear Laplacian (p = 2) of Kigami. In the nonlinear case, the definition only gives a multivalued operator, although under mild conjectures it becomes single valued. The main result is that we can always solve Delta(p)u = f with prescribed boundary values by solving an equivalent minimization problem. We use this to obtain numerical approximations to the solution. We also study properties of p-harmonic functions.