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Partial regularity results for vector valued functions which minimize certain functionals having non quadratic growth under smooth side conditions.
Phase transition with supercooling
L'articolo riassume il quadro dei risultati noti circa il cosiddetto problema di Stefan con sopraraffreddamento. Con ciò si intende in senso lato l'estensione del modello di Stefan a quei casi in cui la temperatura della fase liquida (solida) non è confinata al di sopra (sotto) di quella di cambiamento di fase, supposta costante. La nostra discussione è prevalentemente rivolta allo sviluppo di singolarità (non limitatezza della velocità dell'interfaccia, ecc.), al modo di prevederle, di prevenirle...
Poches de tourbillon singulières dans un fluide faiblement visqueux.
In this paper, we study the singular vortex patches in the two-dimensional incompressible Navier-Stokes equations. We show, in particular, that if the initial vortex patch is C1+s outside a singular set Σ, so the velocity is, for all time, lipschitzian outside the image of Σ through the viscous flow. In addition, the correponding lipschitzian norm is independent of the viscosity. This allows us to prove some results related to the inviscid limit for the geometric structures of the vortex patch.
Problème de Cauchy analytique à données ramifiées
Problème de Cauchy ramifié en théorie des faisceaux (d'après un travail avec P. Schapira)
Prolongement des solutions holomorphes de problèmes aux limites
Dans cet article, on démontre, par des techniques d’analyse microlocale analytique, un résultat local de prolongement holomorphe pour les solutions de problèmes aux limites. Afin de minimiser le domaine dans lequel on suppose holomorphes au départ ces solutions, un résultat préliminaire de prolongement pour les solutions d’équations aux dérivées partielles a été obtenu, par la technique des déformations non caractéristiques, utilisant un théorème de Zerner dont on donne ici une nouvelle démonstration....
Propagation de l'analyticité des solutions de systèmes hyperboliques non-linéaires.
Propagation de l'analyticité locale pour l'équation d'Euler
Propagation des singularités au bord d’ouverts de
Propagation des singularités pour les équations aux dérivées partielles non linéaires
Propagation des singularités pour les équations des ondes semi-linéaires
Propagation of analytic singularities for the Schrödinger Equation
Propagation of analyticity of solutions to the Cauchy problem for Kirchhoff type equations
We shall give the local in time existence of the solutions in Gevrey classes to the Cauchy problem for Kirhhoff equations of -laplacian type and investigate the propagation of analyticity of solutions for real analytic deta. When , his equation as the global real analytic solution for the real analytic initial data.
Propagation of singularities and local solvability in Gevrey classes
Propagation of singularities and maximal functions in the plane.
Propagation of singularities for a first order semi-linear system in
Propagation of singularities in many-body scattering in the presence of bound states
In these lecture notes we describe the propagation of singularities of tempered distributional solutions of , where is a many-body hamiltonian , , , and is not a threshold of , under the assumption that the inter-particle (e.g. two-body) interactions are real-valued polyhomogeneous symbols of order (e.g. Coulomb-type with the singularity at the origin removed). Here the term “singularity” provides a microlocal description of the lack of decay at infinity. Our result is then that the...
Propagation, reflection and refraction of singularities for a hyperbolic transmission problem in two adjacent angular regions
Pseudodifferential operators with multiple characteristics and Gevrey classes