Rectifiability of flat chains.
Regolarità di frontiere minimali con ostacoli sottili
Regolarità per il problema della goccia appoggiata
Regularity at infinity for area-minimizing hypersurfaces in hyperbolic space.
Regularity of minimal boundaries with obstacles
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 the Singular Sets of Two-Dimensional Area-Minimizing Flat Chains Modulo 3 in R3.
Regularity results for minimizing currents with a free boundary.
Relating phase field and sharp interface approaches to structural topology optimization
A phase field approach for structural topology optimization which allows for topology changes and multiple materials is analyzed. First order optimality conditions are rigorously derived and it is shown via formally matched asymptotic expansions that these conditions converge to classical first order conditions obtained in the context of shape calculus. We also discuss how to deal with triple junctions where e.g. two materials and the void meet. Finally, we present several numerical results for...
Relaxation and Integral Representation for Functionals of Linear Growth on Metric Measure spaces
This article studies an integral representation of functionals of linear growth on metric measure spaces with a doubling measure and a Poincaré inequality. Such a functional is defined via relaxation, and it defines a Radon measure on the space. For the singular part of the functional, we get the expected integral representation with respect to the variation measure. A new feature is that in the representation for the absolutely continuous part, a constant appears already in the weighted Euclidean...
Relaxation of isotropic functionals with linear growth defined on manifold constrained Sobolev mappings
In this paper we study the lower semicontinuous envelope with respect to the -topology of a class of isotropic functionals with linear growth defined on mappings from the -dimensional ball into that are constrained to take values into a smooth submanifold of .
Relaxation of isotropic functionals with linear growth defined on manifold constrained Sobolev mappings
In this paper we study the lower semicontinuous envelope with respect to the L1-topology of a class of isotropic functionals with linear growth defined on mappings from the n-dimensional ball into that are constrained to take values into a smooth submanifold of .
Remarks on -stability of the conformal set in higher dimensions
Rotating drops in a vessel. Existence of local minima