On aspects of the normalized infinity Laplacian on Finsler manifolds. (English) Zbl 07900460
Summary: In the context of Finsler manifolds, the paper explores the existence, asymptotic boundary behavior, and uniqueness of viscosity solutions to infinite boundary-value problems associated with the normalized infinite Laplacian in relatively compact subsets. The equation under consideration incorporates lower-order terms featuring non-linear gradient terms. To achieve this objective, we study Dirichlet problems with continuous boundary data and establish a comparison principle, which is of independent significance.
MSC:
| 35J70 | Degenerate elliptic equations |
| 35J60 | Nonlinear elliptic equations |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
| 35B40 | Asymptotic behavior of solutions to PDEs |
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