Radial basis function level set method for structural optimization
Rectifiabilité quantifié et le problème du voyageur de commerce
Rectifiability and perimeter in step 2 groups
Rectifiability and perimeter in step 2 Groups
We study finite perimeter sets in step 2 Carnot groups. In this way we extend the classical De Giorgi’s theory, developed in Euclidean spaces by De Giorgi, as well as its generalization, considered by the authors, in Heisenberg groups. A structure theorem for sets of finite perimeter and consequently a divergence theorem are obtained. Full proofs of these results, comments and an exhaustive bibliography can be found in our preprint (2001).
Rectifiability of flat chains.
Regolarità di frontiere minimali con ostacoli sottili
Regolarità per il problema della goccia appoggiata
Regular mappings between dimensions
The notions of Lipschitz and bilipschitz mappings provide classes of mappings connected to the geometry of metric spaces in certain ways. A notion between these two is given by regular mappings (reviewed in Section 1), in which some non-bilipschitz behavior is allowed, but with limitations on this, and in a quantitative way. In this paper we look at a class of mappings called (s, t)-regular mappings. These mappings are the same as ordinary regular mappings when s = t, but otherwise they behave somewhat...
Régularité Lipschitzienne des Géodésiques Minimisantes pour Quelques Distributions Affines
2000 Mathematics Subject Classification: 49J15, 49J30, 53B50.In the context of sub-Riemannian geometry and the Lipschitzian regularity of minimizers in control theory, we investigate some properties of minimizing geodesics for certain affine distributions. In particular, we consider the case of a generalized H2-strong affine distribution and the case of an affine Plaff system of maximal class.
Regularity and Finiteness of Solutions to the Free Boundary Problem for Minimal Surfaces.
Regularity at infinity for area-minimizing hypersurfaces in hyperbolic space.
Regularity at the free boundary of two-dimensional stationary harmonic maps
Regularity of a Minimal Surface at its Free Boundary.
Regularity of minimal boundaries with obstacles
Regularity of optimal shapes for the Dirichlet’s energy with volume constraint
In this paper, we prove some regularity results for the boundary of an open subset of which minimizes the Dirichlet’s energy among all open subsets with prescribed volume. In particular we show that, when the volume constraint is “saturated”, the reduced boundary of the optimal shape (and even the whole boundary in dimension 2) is regular if the state function is nonnegative.
Regularity of optimal shapes for the Dirichlet's energy with volume constraint
In this paper, we prove some regularity results for the boundary of an open subset of which minimizes the Dirichlet's energy among all open subsets with prescribed volume. In particular we show that, when the volume constraint is “saturated”, the reduced boundary of the optimal shape (and even the whole boundary in dimension 2) is regular if the state function is nonnegative.
Regularity of optimal transport maps on multiple products of spheres
This article addresses regularity of optimal transport maps for cost=“squared distance” on Riemannian manifolds that are products of arbitrarily many round spheres with arbitrary sizes and dimensions. Such manifolds are known to be non-negatively cross-curved. Under boundedness and non-vanishing assumptions on the transfered source and target densities we show that optimal maps stay away from the cut-locus (where the cost exhibits singularity), and obtain injectivity and continuity of optimal maps....
Regularity of sets with constant intrinsic normal in a class of Carnot groups
In this Note, we define a class of stratified Lie groups of arbitrary step (that are called “groups of type ” throughout the paper), and we prove that, in these groups, sets with constant intrinsic normal are vertical halfspaces. As a consequence, the reduced boundary of a set of finite intrinsic perimeter in a group of type is rectifiable in the intrinsic sense (De Giorgi’s rectifiability theorem). This result extends the previous one proved by Franchi, Serapioni & Serra Cassano in step...
Regularity of the optimal shape for the first eigenvalue of the laplacian with volume and inclusion constraints
Regularity of the Singular Sets of Two-Dimensional Area-Minimizing Flat Chains Modulo 3 in R3.