Regularity for non-uniformly elliptic systems and application to some variational integrals.
Regularity for vector valued minimizers of some anisotropic integral functionals.
Regularity of displacement solutions in Hencky plasticity. II: The main result
The aim of this paper is to study the problem of regularity of displacement solutions in Hencky plasticity. Here, a non-homogeneous material is considered, where the elastic-plastic properties change discontinuously. In the first part, we have found the extremal relation between the displacement formulation defined on the space of bounded deformation and the stress formulation of the variational problem in Hencky plasticity. In the second part, we prove that the displacement...
Regularity of displacement solutions in Hencky plasticity. I: The extremal relation
The aim of this paper is to study the problem of regularity of displacement solutions in Hencky plasticity. A non-homogeneous material whose elastic-plastic properties change discontinuously is considered. We find (in an explicit form) the extremal relation between the displacement formulation (defined on the space of bounded deformation) and the stress formulation of the variational problem in Hencky plasticity. This extremal relation is used in the proof of the regularity of displacements. ...
Regularity of Lipschitz minima
Regularity of minima: an invitation to the Dark Side of the Calculus of Variations
I am presenting a survey of regularity results for both minima of variational integrals, and solutions to non-linear elliptic, and sometimes parabolic, systems of partial differential equations. I will try to take the reader to the Dark Side...
Regularity of minima of variational integrals
Regularity of minimizers for a class of membrane energies
Regularity of minimizers for nonconvex vectorial integrals with growth via relaxation methods.
Regularity of minimizers in optimal control
Regularity of minimizers of the calculus of variations in Carnot groups via hypoellipticity of systems of Hörmander type
We prove the hypoellipticity for systems of Hörmander type with constant coefficients in Carnot groups of step 2. This result is used to implement blow-up methods and prove partial regularity for local minimizers of non-convex functionals, and for solutions of non-linear systems which appear in the study of non-isotropic metric structures with scalings. We also establish estimates of the Hausdorff dimension of the singular set.
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 parabolic hemivariational inequalities with boundary conditions.
Regularity of solutions fo a degenerate elliptic variational problem.
Regularity of solutions for arbitrary order variational inequalities with general convex sets
Regularity of solutions in plasticity. I: Continuum
The aim of this paper is to study the problem of regularity of solutions in Hencky plasticity. We consider a non-homogeneous material whose elastic-plastic properties change discontinuously. We prove that the displacement solutions belong to the space if the stress solution is continuous and belongs to the interior of the set of admissible stresses, at each point. The part of the functional which describes the work of boundary forces is relaxed.
Regularity of solutions in plasticity. II: Plates
The aim of this paper is to study the problem of regularity of displacement solutions in Hencky plasticity. We consider a plate made of a non-homogeneous material whose elastic-plastic properties change discontinuously. We prove that the displacement solutions belong to the space if the stress solution is continuous and belongs to the interior of the set of admissible stresses, at each point. The part of the functional which describes the work of boundary forces is relaxed.
Regularity properties of free discontinuity sets