On the strong maximum principle and the large time behavior of generalized mean curvature flow with the Neumann boundary condition
The problem studied can be written as \[ \begin{cases} u_t=|\nabla u|\cdot \text{div}({\nabla u\over|\nabla u|})\quad &\text{in }\Omega\times (0,\infty),\\ {\partial u\over\partial n}= 0\quad &\text{on }\partial\Omega\times (0,\infty),\\ u(x,0)= a(x).\end{cases} \] Here \(\Omega\) is a smooth convex domain in \(\mathbb{R}^n\). They prove a convergence result and a maximum principle for viscosity solutions.
scientific article; zbMATH DE number 1288032