The strong maximum principle for Schrödinger operators on fractals

Demonstratio mathematica

article

Marius V. Ionescu¹  Kasso A. Okoudjou²  Luke G. Rogers³ 

[1] Department of Mathematics, United States Naval Academy;Department of Mathematics and Norbert Wiener Center, University of Maryland, College Park;Department of Mathematics, University of Connecticut

关键词: analysis on fractals;    Harnack’s inequality;    maximum principles Sierpiński gasket;    Schrödinger operators;   

DOI  :  10.1515/dema-2019-0034

学科分类：外科医学

来源: De Gruyter

【 摘 要 】

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.

【 授权许可】

CC BY