Convergence of Allen–Cahn equations to De Giorgi’s multiphase mean curvature flow
Abstract
Abstract This paper presents a conditional convergence result of solutions to the Allen–Cahn equation with multiwell potentials to a De Giorgi-type $$ {{\,\textrm{BV}\,}}$$ BV -solution to multiphase mean curvature flow. Moreover, we show that De Giorgi-type $$ {{\,\textrm{BV}\,}}$$ BV -solutions are De Giorgi-type varifold solutions, and thus our solution is unique in a weak-strong sense.
Fields of Study & Subjects
Geometry and complex manifolds
Geometric Analysis and Curvature Flows
Analytic and geometric function theory
Publication details
- Journal / source
- Journal of Evolution Equations
- Publisher
- Springer Science and Business Media LLC
- Volume
- 26
- Issue
- 2
- Publication date
- 7 May 2026
- Language
- EN