A nonlocal 1-laplacian problem and median values
In this paper, we study solutions to a nonlocal 1-Laplacian equation given by [EQUATION PRESENTED] with u(x) = ψ (x) for x 2 ∈ ωJ\\ω. We introduce two notions of solution and prove that the weaker of the two concepts is equivalent to a nonlocal median value property, where the median is determined b...
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | JOUR |
| Materias: | |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_02141493_v60_n_p27_Mazon |
| Aporte de: |
| Sumario: | In this paper, we study solutions to a nonlocal 1-Laplacian equation given by [EQUATION PRESENTED] with u(x) = ψ (x) for x 2 ∈ ωJ\\ω. We introduce two notions of solution and prove that the weaker of the two concepts is equivalent to a nonlocal median value property, where the median is determined by a measure related to J. We also show that solutions in the stronger sense are nonlocal analogues of local least gradient functions, in the sense that they minimize a nonlocal functional. In addition, we prove that solutions in the stronger sense converge to least gradient solutions when the kernel J is appropriately rescaled. |
|---|