We deal with existence and uniqueness for continuous solutions to the equation for with a prescribed datum for . Here stands for the median value of in the set . In addition we show that when we consider the family of sets then the corresponding solutions converge as to the unique viscosity solution to the local degenerate parabolic PDE, , where is the orthogonal subspace to and is a positive constant. This PDE turns out to be the equation that describes the mean curvature flow in its level sets formulation.
Cite this article
Gaston Beltritti, Julio D. Rossi, Nonlocal Averages in Space and Time Given by Medians and the Mean Curvature Flow. Z. Anal. Anwend. 39 (2020), no. 2, pp. 223–243DOI 10.4171/ZAA/1658