Convergence of Thresholding Energies for Anisotropic Mean Curvature Flow on Inhomogeneous Obstacle
Abstract
Abstract. We extend the analysis by Esedoḡlu and Otto (2015) of thresholding energies for the celebrated multiphase Bence–Merriman–Osher algorithm for computing mean curvature flow of interfacial networks to the case of differing space-dependent anisotropies. In particular, we address the special setting of an obstacle problem, where anisotropic particles move on an inhomogeneous substrate. By suitable modification of the surface energies, we construct an approximate energy that uses a single convolution kernel and is monotone with respect to the convolution width. This allows us to prove that the approximate energies [Formula: see text]-converge to their sharp interface counterpart.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Geometry and complex manifolds
advanced mathematical theories
Publication details
- Journal / source
- SIAM Journal on Mathematical Analysis
- Volume
- 58
- Issue
- 3
- Pages
- 2475–2505
- Publication date
- 13 May 2026
- Language
- EN