Resumen de A nonlocal 1-Laplacian problem and median values

José Manuel Mazón Ruiz , Mayte Pérez Llanos, Julio D. Rossy, José Julián Toledo Melero

• 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.