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...
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| Format: | Article |
| Language: | English |
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De Gruyter
2019-09-01
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| Series: | Demonstratio Mathematica |
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| Online Access: | https://doi.org/10.1515/dema-2019-0034 |
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doaj-0963a715ca47455388b2d59d317efc7c2021-07-01T05:21:52ZengDe GruyterDemonstratio Mathematica2391-46612019-09-0152140440910.1515/dema-2019-0034dema-2019-0034The strong maximum principle for Schrödinger operators on fractalsIonescu Marius V.0Okoudjou Kasso A.1Rogers Luke G.2Department of Mathematics, United States Naval Academy, Annapolis, MD, 21402-5002, USADepartment of Mathematics and Norbert Wiener Center, University of Maryland, College Park, MD 20742, USADepartment of Mathematics, University of Connecticut, Storrs, CT 06269-1009, USAWe 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.https://doi.org/10.1515/dema-2019-0034analysis on fractalsharnack’s inequalitymaximum principles sierpiński gasketschrödinger operatorsprimary 35j15, 28a80secondary 35j25 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Ionescu Marius V. Okoudjou Kasso A. Rogers Luke G. |
| spellingShingle |
Ionescu Marius V. Okoudjou Kasso A. Rogers Luke G. The strong maximum principle for Schrödinger operators on fractals Demonstratio Mathematica analysis on fractals harnack’s inequality maximum principles sierpiński gasket schrödinger operators primary 35j15, 28a80 secondary 35j25 |
| author_facet |
Ionescu Marius V. Okoudjou Kasso A. Rogers Luke G. |
| author_sort |
Ionescu Marius V. |
| title |
The strong maximum principle for Schrödinger operators on fractals |
| title_short |
The strong maximum principle for Schrödinger operators on fractals |
| title_full |
The strong maximum principle for Schrödinger operators on fractals |
| title_fullStr |
The strong maximum principle for Schrödinger operators on fractals |
| title_full_unstemmed |
The strong maximum principle for Schrödinger operators on fractals |
| title_sort |
strong maximum principle for schrödinger operators on fractals |
| publisher |
De Gruyter |
| series |
Demonstratio Mathematica |
| issn |
2391-4661 |
| publishDate |
2019-09-01 |
| description |
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. |
| topic |
analysis on fractals harnack’s inequality maximum principles sierpiński gasket schrödinger operators primary 35j15, 28a80 secondary 35j25 |
| url |
https://doi.org/10.1515/dema-2019-0034 |
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