The strong maximum principle for Schrödinger operators on fractals
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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2019-09-01
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| Series: | Demonstratio Mathematica |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/dema-2019-0034 |
| Summary: | 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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| ISSN: | 2391-4661 |