Hierarchical convergence of a double-net algorithm for equilibrium problems and variational inequality problems.
High order inverse function theorems
High order necessary optimality conditions.
Higher integrability of determinants and weak convergence in L1.
Higher order Grassmann fibrations and the calculus of variations.
Higher order variational inequalities with non-standard growth conditions in dimension two: plates with obstacles.
Higher order variational problems on two-dimensional domains.
Higher-order phase transitions with line-tension effect
The behavior of energy minimizers at the boundary of the domain is of great importance in the Van de Waals-Cahn-Hilliard theory for fluid-fluid phase transitions, since it describes the effect of the container walls on the configuration of the liquid. This problem, also known as the liquid-drop problem, was studied by Modica in [Ann. Inst. Henri Poincaré, Anal. non linéaire 4 (1987) 487–512], and in a different form by Alberti et al. in [Arch. Rational Mech. Anal.u is a scalar density function and...
Higher-order phase transitions with line-tension effect
The behavior of energy minimizers at the boundary of the domain is of great importance in the Van de Waals-Cahn-Hilliard theory for fluid-fluid phase transitions, since it describes the effect of the container walls on the configuration of the liquid. This problem, also known as the liquid-drop problem, was studied by Modica in [Ann. Inst. Henri Poincaré, Anal. non linéaire4 (1987) 487–512], and in a different form by Alberti et al. in [Arch. Rational Mech. Anal.144 (1998) 1–46] for a first-order...
Higher-order weakly generalized adjacent epiderivatives and applications to duality of set-valued optimization.
High-order angles in almost-Riemannian geometry
Let and be two smooth vector fields on a two-dimensional manifold . If and are everywhere linearly independent, then they define a Riemannian metric on (the metric for which they are orthonormal) and they give to the structure of metric space. If and become linearly dependent somewhere on , then the corresponding Riemannian metric has singularities, but under generic conditions the metric structure is still well defined. Metric structures that can be defined locally in this way...
High-order variations and small-time local attainability
High-performance simulation-based algorithms for an alpine ski racer's trajectory optimization in heterogeneous computer systems
Effective, simulation-based trajectory optimization algorithms adapted to heterogeneous computers are studied with reference to the problem taken from alpine ski racing (the presented solution is probably the most general one published so far). The key idea behind these algorithms is to use a grid-based discretization scheme to transform the continuous optimization problem into a search problem over a specially constructed finite graph, and then to apply dynamic programming to find an approximation...
Hölder continuity conditions for the solvability of Dirichlet problems involving functionals with free discontinuities
Hölder continuity of minimzers of functionals with variable growth exponent.
Hölder continuity results for a class of functionals with non-standard growth
We prove regularity results for real valued minimizers of the integral functional under non-standard growth conditions of -type, i.e. under sharp assumptions on the continuous function .
Hölder regularity of three-dimensional minimal cones in ℝⁿ
We show the local Hölder regularity of Almgren minimal cones of dimension 3 in ℝⁿ away from their centers. The proof is almost elementary but we use the generalized theorem of Reifenberg. In the proof, we give a classification of points away from the center of a minimal cone of dimension 3 in ℝⁿ, into types ℙ, 𝕐 and 𝕋. We then treat each case separately and give a local Hölder parameterization of the cone.
Hölder regularity of two-dimensional almost-minimal sets in
We give a different and probably more elementary proof of a good part of Jean Taylor’s regularity theorem for Almgren almost-minimal sets of dimension in . We use this opportunity to settle some details about almost-minimal sets, extend a part of Taylor’s result to almost-minimal sets of dimension in , and give the expected characterization of the closed sets of dimension in that are minimal, in the sense that for every closed set such that there is a bounded set so that out...
Homogénéisation
Homogénéisation de frontières par épi-convergence en élasticité linéaire