Thomas Lachand-Robert

Newton's problem of the body of minimal resistance under a single-impact assumption

Abstract. We consider the problem of the body of minimal resistance as formulated in [2], Sect. 5: minimize

A numerical approach to variational problems subject to convexity constraint

F(u):=\int_\Omega dx/(1+|\nabla u(x)|^2)

Functions and Domains Having Minimal Resistance Under a Single-Impact Assumption

, where

Extremal points of a functional on the set of convex functions

\Omega

An example of non-convex minimization and an application to Newton's problem of the body of least resistance

is the unit disc of

H1-projection into the set of convex functions : a saddle-point formulation

{\mathbb R}^2

Minimisation de fonctionnelles dans un ensemble de fonctions convexes

, in the class of radial functions

Régularité des solutions d'un problème variationnel sous contrainte de convexité

u:\Omega\to[0,M]

Representation of the polar cone of convex functions and applications

satisfying a geometrical property (1), corresponding to a single-impact assumption (

The minimum of quadratic functionals of the gradient on the set of convex functions

M>0