Adaptive Newton-like method for shape optimization
Affine maximal hypersurfaces
This paper is part of the autumn school on "Variational problems and higher order PDEs for affine hypersurfaces". We discuss affine Bernstein problems and complete constant mean curvature surfaces in equiaffine differential geometry.
Allard type regularity results for varifolds with free boundaries
Almost Every Curve in R3 Bounds a Unique Area Minimizing Surface.
An a Priori Estimate for the Oscillation of the Normal to a Hypersurface Whose First and Second Variation With Respect to an Elliptic Integrand is Controlled.
An algebraic characterization of quasi-Möbius homeomorphisms. (Une caractérisation algébrique des homéomorphismes quasi-Möbius.)
An asymptotic condition for variational points of nonquadratic functionals
An Embedding Theorem in the Calculus of Variations for Multiple Integrals.
An existence result for a free boundary problem for the -Laplace operator.
An existence result for an interior electromagnetic casting problem
This paper deals with an interior electromagnetic casting (free boundary) problem. We begin by showing that the associated shape optimization problem has a solution which is of class C 2. Then, using the shape derivative and the maximum principle, we give a sufficient condition that the minimum obtained solves our problem.
An existence theorem for a non-regular variational problem.
An isoperimetric inequality in R3
An optimal estimate of the free boundary of a minima surface.
An optimal matching problem
Given two measured spaces and , and a third space , given two functions and , we study the problem of finding two maps and such that the images and coincide, and the integral is maximal. We give condition on and for which there is a unique solution.
An optimal matching problem
Given two measured spaces and , and a third space Z, given two functions u(x,z) and v(x,z), we study the problem of finding two maps and such that the images and coincide, and the integral is maximal. We give condition on u and v for which there is a unique solution.
An optimal shape design problem for a hyperbolic hemivariational inequality
In this paper we consider hemivariational inequalities of hyperbolic type. The existence result for hemivariational inequality is given and the existence theorem for the optimal shape design problem is shown.
An optimum design problem in magnetostatics
In this paper, we are interested in finding the optimal shape of a magnet. The criterion to maximize is the jump of the electromagnetic field between two different configurations. We prove existence of an optimal shape into a natural class of domains. We introduce a quasi-Newton type algorithm which moves the boundary. This method is very efficient to improve an initial shape. We give some numerical results.
An Optimum Design Problem in Magnetostatics
In this paper, we are interested in finding the optimal shape of a magnet. The criterion to maximize is the jump of the electromagnetic field between two different configurations. We prove existence of an optimal shape into a natural class of domains. We introduce a quasi-Newton type algorithm which moves the boundary. This method is very efficient to improve an initial shape. We give some numerical results.
Analysis of a one-dimensional variational model of the equilibrium shapel of a deformable crystal
Analysis of a one-dimensional variational model of the equilibrium shapel of a deformable crystal
The equilibrium configurations of a one-dimensional variational model that combines terms expressing the bulk energy of a deformable crystal and its surface energy are studied. After elimination of the displacement, the problem reduces to the minimization of a nonconvex and nonlocal functional of a single function, the thickness. Depending on a parameter which strengthens one of the terms comprising the energy at the expense of the other, it is shown that this functional may have a stable absolute...