Thep-Laplacian on the Sierpinski gasket
Robert S. Strichartz, Carto Wong · Nonlinearity · 2004
We define a nonlinear p -Laplacian operator, Δ p , on the Sierpinski gasket, for 1 < p < ∞ , 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 Δ 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.