A unique continuation property for the level set equation

2018/06/01 by Strehlke, Nick
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1806.00389

Abstract

We prove the following unique continuation result: if a solution to the level set equation for mean curvature flow in a mean-convex domain agrees to infinite order at the point where it attains its maximum with the solution for a ball, then it agrees everywhere and the domain is a ball.

Related

• Asymptotics for the level set equation near a maximum
• Level set mean curvature flow with Neumann boundary conditions
• Remarks on large time behavior of level-set mean curvature flow\n equations with driving and source terms
• Singularities of mean convex level set flow in general ambient manifolds
• Motion Of Level Set By General Curvature