Degenerate parabolic PDEs with discontinuities and generalized evolutions of surfaces
Hitoshi Ishii · Advances in Differential Equations · 1996
We establish comparison theorems for solutions of degenerate parabolic partial differential equations with discontinuities (or singularities). The results are used to define the generalized evolutions of sets generated by geometric partial differential equations with discontinuities. These results generalize recent results obtained by Ohnuma-Sato ([13]) and Gurtin-Soner-Souganidis ([11]).