On the behaviour of \(\infty\)-harmonic functions near isolated points. (English) Zbl 1053.31003
The author obtains some informations about \(\infty\)-harmonic functions in the setting of viscosity solutions. He considers bounded solutions and solutions that are only locally bounded near exceptional points.
He makes no use of approximating sequences but of the Harnack inequality and frequent use of the comparison principle. Particulary interesting is the appendix containing an example of a strongly singular solution and the study of the case of the ball.
He makes no use of approximating sequences but of the Harnack inequality and frequent use of the comparison principle. Particulary interesting is the appendix containing an example of a strongly singular solution and the study of the case of the ball.
Reviewer: Maria Alessandra Ragusa (Catania)
MSC:
| 31B05 | Harmonic, subharmonic, superharmonic functions in higher dimensions |
| 31C05 | Harmonic, subharmonic, superharmonic functions on other spaces |
| 49L25 | Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games |
| 31B35 | Connections of harmonic functions with differential equations in higher dimensions |
| 31B25 | Boundary behavior of harmonic functions in higher dimensions |
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