Lipschitz Continuity of Laplacian Eigenfunctions on a class of postcritically finite (PCF) self-similar sets

Group Members

Benjamin YorkAnchala Krishnan


Gamal MograbyChristopher Hayes, Luke Rogers.


We prove a general result for Lipschitz and Hölder continuity of functions defined on a class of postcritically finite (PCF) self-similar sets. Intuition for this theorem comes from formulating arguments on the unit interval, which is well understood in a classical setting. We generalize these results for many kinds of self-similar sets endowed with different measures and metrics. As a corollary to this general result, we prove that eigenfunctions of the Laplacian on the harmonic Sierpinski Gasket are Lipschitz continuous.