Espaces de fonctions et distributions du type de Gevrey et problèmes aux limites paraboliques

Résumé Le travail est résumé dans l'Introduction.     

Measures of controllability

We introduce here a new notion, the measure ofcontrollability aimed at expressing that one system is “more controllable” than another one. First estimates are given.     

Solutions of Hartree-Fock equations for Coulomb systems

This paper deals with the existence of multiple solutions of Hartree-Fock equations for Coulomb systems and related equations such as the Thomas-Fermi-Dirac-Von Weizäcker equation.Partially supported by CEA-DAM     

Problèmes aux limites non homogènes (VII)

Annali di Matematica Pura ed Applicata (1923 -) -     

Sur la stabilisation de certains problèmes mal posés

Milan Journal of Mathematics - Si indica un metodo di stabilizzazione per i problemi mal posti e si porge, fra l’altro, qualche esempio relativo alle equazioni ellittiche e paraboliche. Le...     

Convergent difference schemes for nonlinear parabolic equations and mean curvature motion

Summary. Explicit finite difference schemes are given for a collection of parabolic equations which may have all of the following complex features: degeneracy, quasilinearity, full nonlinearity, and singularities. In particular, the equation of “motion by mean curvature” is included. The schemes are monotone and consistent, so that convergence is guaranteed by the general theory of approximation of viscosity solutions of fully nonlinear problems. In addition, an intriguing new type of nonlocal problem is analyzed which is related to the schemes, and another very different sort of approximation is presented as well. Received January 10, 1995     

Optimisation pour certaines classes d'équations d'évolution non linéaires

Résumé Comme dans l'Introduction.     

On the Hamilton-Jacobi-Bellman equations

We consider general problems of optimal stochastic control and the associated Hamilton-Jacobi-Bellman equations. We recall first the usual derivation of the Hamilton-Jacobi-Bellman equations from the Dynamic Programming Principle. We then show and explain various results, including (i) continuity results for the optimal cost function, (ii) characterizations of the optimal cost function as the maximum subsolution, (iii) regularity results, and (iv) uniqueness results. We also develop the recent notion of viscosity solutions of Hamilton-Jacobi-Bellman equations.     

Binding of atoms and stability of molecules in hartree and thomas-fermi type theories.

This paper is the fourth of a series devoted to the study of the stability of general molecular systems in Thomas-Fermi or Hartree type models. In the preceding part, we proved the bindingof arbitrary neutral systems for Thomas-Fermi type theories and of planar neutral systems forthe Hartree model. In this part, we manage to get rid of this restriction and thus, prove thebinding and the stability of arbitrary neutral systems for the Hartree model.