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- Ricardo H. Nochetto, Maurizio Paolini, Claudio Verdi
- SIAM J. Scientific Computing
- 1991

- Maurizio Paolini
- Math. Comput.
- 1997

Solutions of the so-called prescribed curvature problem minA⊆Ω PΩ(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)

For a nonsmooth positively one homogeneous convex function

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)

- Maurizio Paolini
- 1998

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 diffused interface approximation via a bistable reaction-diffusion equation which is then discretized by means of finite elements in space and forward… (More)

In this paper we study the nonconvex anisotropic mean curvature flow of a hypersurface. 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 geometric… (More)

- Giovanni Bellettini, Valentina Beorchia, Maurizio Paolini
- Journal of Mathematical Imaging and Vision
- 2008

We introduce and study a two-dimensional variational model for the reconstruction of a smooth generic solid shape E, which may handle the self-occlusions and that can be considered as an improvement of the 2.1D sketch of Nitzberg and Mumford (Proceedings of the Third International Conference on Computer Vision, Osaka, 1990). We characterize from the… (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 into R, taking only three values, and jumping on three half-lines meeting at the origin in a triple junction.

We study the asymptotic analysis of a singularly perturbed weakly parabolic system of mequations 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)

- Giovanni Bellettini, Maurizio Paolini, Lucia Tealdi
- 2015

In this paper we estimate the area of the graph of a map u : Ω ⊂ R → R 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 spanning the graphs… (More)