The probabilistic characterization of weakly harmonic maps with respect to non-local Dirichlet forms
| Autor: | Okazaki, Fumiya |
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| Jazyk: | angličtina |
| Rok vydání: | 2023 |
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| Popis: | We characterize weakly harmonic maps with respect to non-local Dirichlet forms by Markov processes and martingales. In particular, we can obtain discontinuous martingales on Riemanian manifolds by inserting symmetric stable processes into fractional harmonic maps in a weak sense. We also consider the continuity of weakly harmonic maps along the paths of Markov processes, which is called the fine continuity. We show that the fine continuity implies the continuity with respect to the Euclidean topology in some situations containing cases of energy minimizing maps. 26 pages |
| Databáze: | OpenAIRE |
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