Maurizio Paolini

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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)
The evolution of a curvature dependent interface is approximated via a singularly perturbed parabolic double obstacle problem with small parameter " > 0. The velocity normal to the front is proportional to its mean curvature plus a forcing term. Optimal interface error estimates of order O(" 2) are derived for smooth evolutions, that is before singularities(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 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)
In this paper we estimate the area of the graph of a map u : Ω ⊂ R 2 → R 2 discontinuous on a segment Ju, with Ju either compactly contained in the bounded open set Ω, or starting and ending on ∂Ω. We characterize A ∞ (u, Ω), the relaxed area functional in a sort of uniform convergence, in terms of the infimum of the area of those surfaces in R 3 spanning(More)