The strong maximum principle for Schrödinger operators on fractals
| Autor: | Marius Ionescu, Kasso A. Okoudjou, Luke G. Rogers |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
harnack’s inequality
secondary 35j25 General Mathematics 010102 general mathematics 01 natural sciences maximum principles sierpiński gasket symbols.namesake Fractal Maximum principle primary 35j15 28a80 0103 physical sciences symbols QA1-939 010307 mathematical physics 0101 mathematics analysis on fractals schrödinger operators Schrödinger's cat Mathematics Mathematical physics |
| Zdroj: | Demonstratio Mathematica, Vol 52, Iss 1, Pp 404-409 (2019) |
| ISSN: | 2391-4661 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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