In this paper we prove some new symmetry results for the extremals of the Caffarelli-Kohn-Nirenberg inequalities, in any dimension larger or equal than 2 .

In this paper, the Hartree-Fock equations are proved to be the non relativistic limit of the Dirac-Fock equations as far as convergence of \stationary states" is concerned. This property is used toâ€¦ (More)

In this paper we extend existing results concerning generalized eigenvalues of Pucciâ€™s extremal operators. In the radial case, we also give a complete description of their spectrum, together with anâ€¦ (More)

This review is devoted to the study of stationary solutions of linear and nonlinear equations from relativistic quantum mechanics, involving the Dirac operator. The solutions are found as criticalâ€¦ (More)

We prove some sharp Hardy type inequalities related to the Dirac operator by elementary, direct methods. Some of these inequalities have been obtained previously using spectral information about theâ€¦ (More)

This paper is devoted to a general min-max characterization of the eigenvalues in a gap of the essential spectrum of a self-adjoint unbounded operator. We prove an abstract theorem, then we apply itâ€¦ (More)

This paper contains a review of available methods for establishing improved interpolation inequalities on the sphere for subcritical exponents. Pushing further these techniques we also establish someâ€¦ (More)

We prove new symmetry results for the extremals of the Caffarelli-Kohn-Nirenberg inequalities in any dimension larger or equal than 2 , in a range of parameters for which no explicit results ofâ€¦ (More)

We review Streater's energy-transport models which describe the temporal evolution of the density and temperature of a cloud of gravitating particles, coupled to a mean eld Poisson equation. Inâ€¦ (More)

We consider a family of Caffarelli-Kohn-Nirenberg interpolation inequalities and weighted logarithmic Hardy inequalities which have been obtained recently as a limit case of the first ones. Weâ€¦ (More)