Solutions faibles des équations elliptiques du deuxième ordre
spaces and rectifiability for Carnot-Carathéodory metrics: an introduction
This paper is meant as a (short and partial) introduction to the study of the geometry of Carnot groups and, more generally, of Carnot-Carathéodory spaces associated with a family of Lipschitz continuous vector fields. My personal interest in this field goes back to a series of joint papers with E. Lanconelli, where this notion was exploited for the study of pointwise regularity of weak solutions to degenerate elliptic partial differential equations. As stated in the title, here we are mainly concerned...
Chaos multiplicatif : un traitement simple et complet de la fonction de partition
Su un teorema di R. H. Martin Jr.
Théorème des résidus asymptotique pour le mouvement brownien sur une surface riemannienne compacte
Asymptotic windings over the trefoil knot.
Consider the group G:=PSL2(R) and its subgroups Γ:= PSL2(Z) and Γ':=DSL2(Z). G/Γ is a canonical realization (up to an homeomorphism) of the complement S3T of the trefoil knot T, and G/Γ' is a canonical realization of the 6-fold branched cyclic cover of S3T, which has a 3-dimensional cohomology of 1-forms. Putting natural left-invariant Riemannian metrics on G, it makes sense to ask which...
Sulla propagazione del calore con velocità finita in un fluido in moto
The author derives the heat propagation equation for forced convection replacing Fourier's law by a constitutive equation generalising Cattaneo's one. Then, for the above mentioned equation, she establishes a uniqueness theorem for finite domains.
Un teorema di unicità per le equazioni di Boussinesq modificate in base all'equazione di Cattaneo-Fox
We establish a uniqueness theorem for the heat propagation by natural convection governed by the Boussinesq equations, when we replace Fourier's law by Cattaneo-Fox' constitutive equation in bounded domains.
Sull'unicità delle soluzioni delle equazioni di Boussmesq modificate in base all'equazione costitutiva di Cattaneo—Fox in un dominio illimitato
Employing the weight function method, we establish a uniqueness theorem for the heat propagation by natural convection governed by the Boussinesq equations when we replace Fourier’s constitutive equation by Cattaneo-Fox’ one, on an exterior domain. We prove the theorem without boundedness assumptions on the velocity gradient and on the temperature.
Propriétés des courbes intégrales de champs de vecteurs et estimations ponctuelles d'équation elliptiques dégénérés
A differentiable isomorphism between Wiener space and path group
Masse des pointes, temps de retour et enroulements en courbure négative
Soient un groupe discret géométriquement fini d’isométries d’une variété de Hadamard pincée et une pointe de l’orbifold associé . Munissant de sa mesure de Patterson-Sullivan , nous obtenons une estimation asymptotique de la masse d’un petit voisinage horocyclique de , moyennant une hypothèse sur la croissance du sous-groupe parabolique associé à , hypothèse qui est réalisée si est symétrique de rang . Nous en déduisons une estimation asymptotique du temps de retour du flot géodésique...
Un algorithme de calcul formel des séries énumératrices de langage linéaire
Compensation couples and isoperimetric estimates for vector fields
How to get rid of one of the weights in a two-weight Poincaré inequality?
We prove that if a Poincaré inequality with two different weights holds on every ball, then a Poincaré inequality with the same weight on both sides holds as well.
Hölder regularity theorem for a class of linear nonuniformly elliptic operators with measurable coefficients
Pointwise estimates for a class of strongly degenerate elliptic operators : a geometrical approach
On group automorphisms fixing subnormal subgroups setwise
In questo lavoro si studiano i gruppi , , degli automorfismi di un gruppo che fissano — come insiemi — tutti i sottogruppi di che risultano essere rispettivamente subnormali, subnormali di difetto al più , oppure che sono compresi tra un sottogruppo caratteristico ed il suo derivato. Si danno condizioni sufficienti affinché tali gruppi siano parasolubili di para-altezza al più 2 o 3. Si generalizzano così risultati da [4], [7], [8], [10].
Some Remarks on Vector Potentials for Maxwell's Equations in Space-Time Carnot Groups
In this paper we prove a -convergence result for time-depending variational functionals in a space-time Carnot group arising in the study of Maxwell's equations in the group. Indeed, a Carnot groups (a connected simply connected nilpotent stratified Lie group) can be endowed with a complex of ``intrinsic'' differential forms that provide the natural setting for a class of ``intrinsic'' Maxwell's equations. Our main results states precisely that a the vector potentials of a solution of Maxwell's...
De Giorgi’s Theorem, for a Class of Strongly Degenerate Elliptic Equations
In questa Nota enunciamo, per una classe di equazioni ellittiche del secondo ordine «fortemente degeneri» a coefficienti misurabili, un teorema di hölderianità delle soluzioni deboli che estende il ben noto risultato di De Giorgi e Nash. Tale risuJtato discende dalle proprietà geometriche di opportune famiglie di sfere associate agli operatori.
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