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The strong maximum principle for Schrödinger operators on fractals

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

Demonstratio Mathematica

2019

Vol. 52, nr 1

404--409

We prove a strong maximum principle for Schrödinger operators defined on a class of postcritically finite 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.