A nonlocal 1-Laplacian problem and median values

1. Mazón, José M.
2. Pérez-Llanos, Mayte
3. Rossy, Julio D.
4. Toledo, Julián

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DOI: 10.5565/10.5565-PUBLMAT 60116 02 DIALNET GOOGLE SCHOLAR lock_openAcceso abierto editor

Otras publicaciones en: Publicacions matematiques

Resumen

In this paper, we study solutions to a nonlocal 1-Laplacian equation. 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.

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