Existence of solutions for a class of heat equations involving the mean curvature operator

The goal of this paper is to show the existence of a bounded variation solution, which is based on the Anzellotti pairing to an evolution problem associated with the mini-mal surface equations. A key ingredient in the proof is to approximate the parabolic minimal surface problem by a quasilinear parabolic problem involving a parameter p > 1, and then by establishing some energy estimates independent of p, we take the limit as p -> 1(+) to obtain the desired result.