Asymptotics for the level set equation near a maximum

2018/06/04 by Strehlke, Nick · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1806.00930

Abstract

We give asymptotics for the level set equation for mean curvature flow on a convex domain near the point where it attains a maximum. It is known that solutions are not necessarily C³, and we recover this result and construct non-smooth solutions which are C³. We also construct solutions having prescribed behavior near the maximum. We do this by analyzing the asymptotics for rescaled mean curvature flow converging to a stationary sphere.

Cited by

• Closed mean curvature flows with prescribed tangent flows
• On the rate of convergence of cylindrical singularity in mean curvature flow

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