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Regularity of displacement solutions in Hencky plasticity. II: The main result

Jarosław L. Bojarski (2011)

Applicationes Mathematicae

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

Jarosław L. Bojarski (2011)

Applicationes Mathematicae

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 minimizers of the calculus of variations in Carnot groups via hypoellipticity of systems of Hörmander type

Luca Capogna, Nicola Garofalo (2003)

Journal of the European Mathematical Society

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

Tanguy Briancon (2004)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we prove some regularity results for the boundary of an open subset of ℝ d 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

Tanguy Briancon (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we prove some regularity results for the boundary of an open subset of d 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

Alessio Figalli, Young-Heon Kim, Robert McCann (2013)

Journal of the European Mathematical Society

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 solutions in plasticity. I: Continuum

Jarosław L. Bojarski (2003)

Applicationes Mathematicae

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 L D ( Ω ) ≡ u ∈ L ¹ ( Ω , ℝ ⁿ ) | ∇ u + ( ∇ u ) T ∈ L ¹ ( Ω , ℝ n × n ) 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

Jarosław L. Bojarski (2004)

Applicationes Mathematicae

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 W 2 , 1 ( Ω ) 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 optimal transportation problems arising in hedonic pricing models

Brendan Pass (2013)

ESAIM: Control, Optimisation and Calculus of Variations

We study a form of optimal transportation surplus functions which arise in hedonic pricing models. We derive a formula for the Ma–Trudinger–Wang curvature of these functions, yielding necessary and sufficient conditions for them to satisfy (A3w). We use this to give explicit new examples of surplus functions satisfying (A3w), of the form b(x,y) = H(x + y) where H is a convex function on ℝn. We also show that the distribution of equilibrium contracts in this hedonic pricing model is absolutely continuous...

Currently displaying 441 – 460 of 597