Catálogo de publicaciones - libros

The solution of the equation div is performed via suitable solutions of the Poisson equation. For this purpose appropriate Sobolev spaces and a certain non-standard negative norm have to be regarded.

Let P be a linear partial differential operator with variable coefficients in the Roumieu class ε(Ω). We prove that if is {ω}-hypoelliptic and has a {ω}-fundamental kernel in Ω, then is surjective on the space ε(Ω).

We construct the fundamental solution for a weakly hyperbolic operator satisfying an intermediate condition between effective hyperbolicity and the Levi condition. By the fundamental solution, we obtain the well-posedness in of the Cauchy problem.

We discuss almost complex perturbations of linear discs. We give precise estimates for the (1, α) norm of these deformations and for the dependence on parameters. In particular, we show how families of such discs give rise to local foliations of the space. Also, if Ω is a domain whose boundary is endowed with at least one negative eigenvector at 0 for the standard structure of ℂ, then small discs with velocity which are analytic for a -perturbation of the structure, have boundary which is contained in ? in a neighborhood of 0. In particular, if the almost complex structure is real analytic, almost holomorphic functions extend along the corresponding foliation of discs.

In reference , among other side results, we prove that the solution of the evolution Navier—Stokes equations (1.1) under the Navier (or slip) boundary condition (1.2) is necessarily regular if the direction of the vorticity is 1/2-Hölder continuous with respect to the space variables. In this notes we show the main steps in the proof and made some comments on the above problem under the non-slip boundary condition (3.2).

We study the exponential decay and the regularity for solutions of elliptic partial differential equations , globally defined in ℝ. In particular, we consider linear operators with polynomial coefficients which are SG-elliptic at infinity. Starting from in the so-called Gelfand-Shilov spaces, the solutions of the equation are proved to belong to the same classes. Proofs are based on a priori estimates and arguments on the Newton polyhedron associated to the operator .

We describe how the Keller-Segel model can be obtained as a driftdiffusion limit of kinetic models. Three different examples with global kinetic solutions yield different chemotactical sensitivity functions, including the case of a constant coefficient, where blow up in the limit may occur, the case with density threshold and an intermediate case for which the corresponding perturbed Keller-Segel models have global solutions.

The aim of this work is to analyze the asymptotic behavior of the eigenmodes of some elliptic eigenvalue problems set on domains becoming unbounded in one or several directions.

We study the behavior for →∞ of the solutions to the Cauchy problem for a strictly hyperbolic second order equation with coefficients periodic in time, or oscillating with a period going to 0.

Two different applications of the operator splitting method are presented here. The first one concerns hyperbolic systems of balance laws in one space dimension: we state the existence and the stability of solutions for initial data with bounded variation. As an example a case of vehicular traffic flow is then considered. The second application concerns abstract nonlinear semigroups in a metric space: we show how a composition of semigroups can be defined, thus generalizing Trotter-Kato product formulas to nonlinear semigroups.