Infinity-Laplacian type equations and their associated Dirichlet problems. (English) Zbl 1442.35124
Summary: In this paper, we study the Dirichlet problem associated with infinity-Laplacian type equations that may exhibit anisotropic character. We identify a broad class of nonlinearities for which the problem may or may not admit viscosity solutions for any continuous boundary data. We also discuss comparison with Finsler cones, which may be of independent interest.
MSC:
| 35J60 | Nonlinear elliptic equations |
| 35J70 | Degenerate elliptic equations |
| 35J75 | Singular elliptic equations |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
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