The Strong Maximum Principle for Schrödinger operators on fractals

by Marius V. Ionescu, Kasso A. Okoudjou, Luke G. Rogers

We prove a strong maximum principle for Schrödinger operators defined on a class of fractal sets and their blowups without boundary. Our primary interest is in weaker regularity conditions than have previously appeared in the literature; in particular we permit both the fractal Laplacian and the potential to be Radon measures on the fractal. As a consequence of our results, we establish a Harnack inequality for solutions of these operators.

Arxiv preprint version

Published version in Demonstratio Mathematica