The strong maximum principle for Schrödinger operators on fractals

Abstract

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.

Keywords

• analysis on fractals
• harnack’s inequality
• maximum principles sierpiński gasket
• schrödinger operators
• primary 35j15, 28a80
• secondary 35j25