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BY 4.0 license Open Access Published by De Gruyter Open Access September 30, 2019

The strong maximum principle for Schrödinger operators on fractals

Marius V. Ionescu, Kasso A. Okoudjou and Luke G. Rogers
From the journal Demonstratio Mathematica

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.

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Received: 2019-02-14
Accepted: 2019-08-05
Published Online: 2019-09-30

© 2019 Marius V. Ionescu et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution 4.0 Public License.

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