The Strong Maximum Principle for Schr\"{o}dinger operators on fractals
Functional Analysis
2019-02-18 v1 Analysis of PDEs
Abstract
We prove a strong maximum principle for Schr\"odinger 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.
Keywords
Cite
@article{arxiv.1902.05584,
title = {The Strong Maximum Principle for Schr\"{o}dinger operators on fractals},
author = {Marius V. Ionescu and Kasso A. Okoudjou and Luke G. Rogers},
journal= {arXiv preprint arXiv:1902.05584},
year = {2019}
}