Majorantes surharmoniques minimales d'une fonction continue

Extending DUNE: The dune-xt modules

We present our effort to extend and complement the core modules of the Distributed and Unified Numerics Environment DUNE (http://dune-project.org) by a well tested and structured collection of utilities and concepts. We describe key elements of our four modules dune-xt-common, dune-xt-grid, dune-xt-la and dune-xt-functions, which aim at further enabling the programming of generic algorithms wit...

Construction De Familles Minimales De Courbes Gauches

Let A be a noetherian local ring, and let C in PA be a family of curves, flat over A. We showed in an earlier paper how to associate to C a locally free sheaf N on PA, and we showed that two families of curves C,C′ are in the same biliaison class if and only if the corresponding sheaves N,N ′ are pseudoisomorphic (generalization of the theorem Rao). In this paper we show how to find all the fla...

Fonctions minimales pour des inégalités de Sobolev anisotropiques

The existence of multiple nonnegative solutions to the anisotropic critical problem − N ∑ i=1 ∂ ∂xi ∣∣∣∣ ∂u ∂xi ∣∣∣∣pi−2 ∂u ∂xi ) = |u|p−2u in R is proved in suitable anisotropic Sobolev spaces. The solutions correspond to extremal functions of a certain best Sobolev constant. The main tool in our study is an adaptation of the well-known concentration-compactness lemma of P.-L. Lions to anisotr...

Minimisation d'une fonction quasi-convexe aléatoire : applications

Modelling a Dune Field

We present a model to describe the collective motion of barchan dunes in a field. Our model is able to reproduce the observation that a typical dune stays confined within a stripe. We also obtain some of the pattern structures which ressemble those observed from aerial photos which we do analyse and compare with the specific field of Laâyounne.