Generalized interface evolution with the Neumann boundary condition
Yoshikazu Giga, Moto-Hiko Sato · Proceedings of the Japan Academy Series A Mathematical Sciences · 1991
1. Introduction.We are concerned with geometric evolution (e.g.motion by mean curvature) of interfaces in a smoothly bounded domain /2 (R") whose boundary 3/2 perpendicularly intersects with interfaces.In [12] the second author extended a level set approach introduced by Chen-Giga-Goto [1] and Evans-Spruck [3] to this type of the Neumann problem and obtained a unique global weak solutions for the initial value problem provided that 2 is convex.This note reports that the convexity assumption of 2 can be removed.The details and proofs will appear elsewhere.