BV solutions for mean curvature flow with constant contact angle: Allen-Cahn approximation and weak-strong uniqueness

2021/12/21 by Sebastian Hensel, Tim Laux, Hensel, Sebastian +1 · 2 citations
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2112.11150

openalex publication_date 2021/12/21 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

We study weak solutions to mean curvature flow satisfying Young's angle condition for general contact angles α∈ (0,π). First, we construct BV solutions using the Allen-Cahn approximation with boundary contact energy as proposed by Owen and Sternberg. Second, we prove the weak-strong uniqueness and stability for this solution concept. The main ingredient for both results is a relative energy, which can also be interpreted as a tilt excess.

Cited by

• Existence of flat flows for volume-preserving mean curvature flow with contact angle
• The vector-valued Allen-Cahn equation with potentials of high-dimensional double-wells under Robin boundary conditions

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