In this paper we will study stability properties for viscosity solutions of geometric equations. We will prove that, if the interface is regular (i.e., it is the boundary of an open set and it is not fat), the signed distance function from the front is stable for geometric perturbations of the equation. This result is based on representation formulas for viscosity solutions in terms of distance functions from the level sets. An application of the previous result to stability of approximation schemes is also presented.
"A stability property for the generalized mean curvature flow equation." Adv. Differential Equations 3 (6) 815 - 846, 1998. https://doi.org/10.57262/ade/1366292550