| Autor: |
Björn, Anders, Björn, Jana, Sjödin, Tomas |
| Rok vydání: |
2016 |
| Předmět: |
|
| Zdroj: |
Rev. Mat. Iberoam. 34 (2018), 1323-1360 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.4171/RMI/1025 |
| Popis: |
We study the Dirichlet problem for p-harmonic functions on metric spaces with respect to arbitrary compactifications. A particular focus is on the Perron method, and as a new approach to the invariance problem we introduce Sobolev-Perron solutions. We obtain various resolutivity and invariance results, and also show that most functions that have earlier been proved to be resolutive are in fact Sobolev-resolutive. We also introduce (Sobolev)-Wiener solutions and harmonizability in this nonlinear context, and study their connections to (Sobolev)-Perron solutions, partly using Q-compactifications. |
| Databáze: |
arXiv |
| Externí odkaz: |
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