Convergence of the natural \(p\)-means for the \(p\)-Laplacian. (English) Zbl 1479.35486
The authors consider a Dirichlet problem for the \(p\)-Laplace operator in a bounded open Lipschitz subset \(\Omega\) of the Euclidean space and prove a uniform approximation result in the closure \(\overline{\Omega}\) of \(\Omega\) for the solution in terms of ‘\(p\)-means’ defined in a neighborhood of \(\overline{\Omega}\) and introduced by M. Ishiwata et al. [Calc. Var. Partial Differ. Equ. 56, No. 4, Paper No. 97, 22 p. (2017; Zbl 1378.35147)]. Then the authors consider a corresponding result in the Heisenberg group.
Reviewer: Massimo Lanza de Cristoforis (Padova)
MSC:
| 35J92 | Quasilinear elliptic equations with \(p\)-Laplacian |
| 35D40 | Viscosity solutions to PDEs |
| 49L20 | Dynamic programming in optimal control and differential games |
| 49L25 | Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games |
| 35R03 | PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. |
Keywords:
\(p\)-Laplacian; natural \(p\)-means; Dirichlet problem; discrete approximations; asymptotic mean value properties; generalized viscosity solutions; Heisenberg groupCitations:
Zbl 1378.35147References:
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