Sur les equations de Monge-Ampere. I.
Introduction
The concentration-compactness principle in the calculus of variations. The limit case, Part II.
This paper is the second part of a work devoted to the study of variational problems (with constraints) in functional spaces defined on domains presenting some (local) form of invariance by a non-compact group of transformations like the dilations in R. This contains for example the class of problems associated with the determination of extremal functions in inequalities like Sobolev inequalities, convolution or trace inequalities... We show how the concentration-compactness principle and method...
The concentration-compactness principle in the calculus of variations. The limit case, Part I.
After the study made in the locally compact case for variational problems with some translation invariance, we investigate here the variational problems (with constraints) for example in R where the invariance of R by the group of dilatations creates some possible loss of compactness. This is for example the case for all the problems associated with the determination of extremal functions in functional inequalities (like for example the Sobolev inequalities). We show here how the concentration-compactness...
Remarques sur les équations linéaires elliptiques du second ordre sous forme divergence dans les domaines non bornés
Si dà una maggiorazione a priori in per le soluzioni di equazioni lineari ellittiche del secondo ordine in domini non limitati.
Remarques sur les équations linéaires elliptiques du second ordre sous forme divergence dans les domaines non bornés
Si dimostra resistenza e l'unicità della soluzione del problema , nel caso in cui è un aperto di non limitato, è un operatore variazionale ellittico del secondo ordine a coefficienti misurabili e limitati e appartiene a .
Un problème de contrôle géométrique et les équations de Hamilton-Jacobi-Bellman
Le problème de Cauchy pour les équations de Hamilton-Jacobi-Bellman
Remarques sur les équations linéaires elliptiques du second ordre sous forme divergence dans les domaines non bornés
Si dà una maggiorazione a priori in per le soluzioni di equazioni lineari ellittiche del secondo ordine in domini non limitati.
Remarques sur les équations linéaires elliptiques du second ordre sous forme divergence dans les domaines non bornés
Si dimostra resistenza e l'unicità della soluzione del problema , nel caso in cui è un aperto di non limitato, è un operatore variazionale ellittico del secondo ordine a coefficienti misurabili e limitati e appartiene a .
Large investor trading impacts on volatility
Homogenization of degenerate second-order PDE in periodic and almost periodic environments and applications
On the existence of a positive solution of semilinear elliptic equations in unbounded domains
Some asymptotic problems in fully nonlinear elliptic equations and stochastic control
Sur les mesures de Wigner.
We study the properties of the Wigner transform for arbitrary functions in L or for hermitian kernels like the so-called density matrices. And we introduce some limits of these transforms for sequences of functions in L, limits that correspond to the semi-classical limit in Quantum Mechanics. The measures we obtain in this way, that we call Wigner measures, have various mathematical properties that we establish. In particular, we prove they satisfy, in linear situations (Schrödinger equations) or...
Diffusive limit for finite velocity Boltzmann kinetic models.
We investigate, in the diffusive scaling, the limit to the macroscopic description of finite-velocity Boltzmann kinetic models, where the rate coefficient in front of the collision operator is assumed to be dependent of the mass density. It is shown that in the limit the flux vanishes, while the evolution of the mass density is governed by a nonlinear parabolic equation of porous medium type. In the last part of the paper we show that our method adapts to prove the so-called Rosseland approximation...
Équations aux dérivées partielles stochastiques nonlinéaires et solutions de viscosité
Fully nonlinear second order elliptic equations with large zeroth order coefficient
We prove the existence of classical solutions to certain fully non-linear second order elliptic equations with large zeroth order coefficient. The principal tool is an estimate asserting that the -norm of the solution cannot lie in a certain interval of the positive real axis.
Une remarque sur les opérateurs non linéaires intervenant dans les inéquations quasi-variationnelles
Convex symmetrization and applications
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