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For a nonsmooth positively one homogeneous convex function
In this paper we study the nonconvex anisotropic mean curvature flow of a hypersur-face. This corresponds to an anisotropic mean curvature flow where the anisotropy has a nonconvex Frank diagram. The geometric evolution law is therefore forward-backward parabolic in character, hence ill-posed in general. We study a particular regularization of this… (More)
We consider the approximation of curvature dependent geometric front evolutions by singularly perturbed parabolic double obstacle problems with small parameter ". We give a simpliied proof of optimal interface error estimates of order O(" 2), valid in the smooth regime, which is based on constructing precise barriers, perturbing the forcing term and… (More)
Solutions of the so-called prescribed curvature problem min A⊆Ω P Ω (A) − A g(x), g being the curvature field, are approximated via a singularly perturbed elliptic PDE of bistable type. For nondegenerate relative minimizers A ⊂⊂ Ω we prove an O(2 | log | 2) error estimate (where stands for the perturbation parameter), and show that this estimate is… (More)
We improve an estimate given by Acerbi and Dal Maso in 1994, concerning the area of the graph of a singular map from the disk of R 2 into R 2 , taking only three values, and jumping on three half-lines meeting at the origin in a triple junction.
In this paper we present a few numerical simulations of a nonsymmetric anisotropic evolution by mean curvature which leads to the so-called fattening of the interface. The numerical simulations are based on a diiused interface approximation via a bistable reaction-diiusion equation which is then discretized by means of nite elements in space and forward… (More)
We study the asymptotic analysis of a singularly perturbed weakly parabolic system of m-equations of anisotropic reaction-diffusion type. Our main result formally shows that solutions to the system approximate a geometric motion of a hypersurface by anisotropic mean curvature. The anisotropy, supposed to be uniformly convex, is explicit and turns out to be… (More)