Anisotropic and crystalline mean curvature flow of mean-convex sets. (English) Zbl 1498.53113
Summary: We consider a variational scheme for the anisotropic and crystalline mean curvature flow of sets with strictly positive anisotropic mean curvature. We show that such condition is preserved by the scheme, and we prove the strict convergence in \(BV\) of the time-integrated perimeters of the approximating evolutions, extending a recent result of De Philippis and Laux to the anisotropic setting. We also prove uniqueness of the “flat flow” obtained in the limit.
MSC:
| 53E10 | Flows related to mean curvature |
| 49Q20 | Variational problems in a geometric measure-theoretic setting |
| 58E12 | Variational problems concerning minimal surfaces (problems in two independent variables) |
| 35A15 | Variational methods applied to PDEs |
| 74E10 | Anisotropy in solid mechanics |
Keywords:
anisotropic mean curvature; strictly positive anisotropic mean curvature; variational scheme; outward minimalityReferences:
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