Sul modulo di continuità alla frontiera della soluzione del problema di Dirichlet relativo ad una classe di operatori parabolici
Strutture subriemanniane in alcuni problemi di Analisi
Vengono presentati alcuni problemi, idee e tecniche sorte nell'ambito della teoria delle equazioni alle derivate parziali del secondo ordine, con forma caratteristica semidefinita positiva e con soggiacenti strutture sub-riemanniane. Se ne traccia lo sviluppo a partire dalla classica teoria delle funzioni armoniche e caloriche, attraverso la teoria del potenziale negli spazi armonici astratti e la teoria della regolarità locale delle soluzioni.
Nonlinear equations on Carnot groups and curvature problems for CR manifolds
We give a short overview of sub-Laplacians on Carnot groups starting from a result by Caccioppoli dated 1934. Then we show that sub-Laplacians on Carnot groups of step one arise in studying curvature problems for manifolds. We restrict our presentation to the cases of the Webster-Tanaka curvature problem for the sphere and of the Levi-curvature equation for strictly pseudoconvex functions.
Sul problema di Dirichlet per equazioni paraboliche del secondo ordine a coefficienti discontinui
We consider the Dirichlet problem for a class of second order linear parabolic operators with discontinuous coefficients in divergence form; some theorems on regularity of boundary points are given.
Su una classe di moltiplicatori di ed applicazioni
We get a class of multipliers which contains, for example, the functions of type , real-valued. Some applications to the spectrum of partial differential operators on are given.
Asymptotic Behavior of Fundamental Solutions and Potential Theory of Prabolic Operators with Variable Coeeficients.
Hölder regularity theorem for a class of linear nonuniformly elliptic operators with measurable coefficients
Dirichlet problem with L-boundary data in contractible domains of Carnot groups
Let be a sub-laplacian on a stratified Lie group . In this paper we study the Dirichlet problem for with -boundary data, on domains which are contractible with respect to the natural dilations of . One of the main difficulties we face is the presence of non-regular boundary points for the usual Dirichlet problem for . A potential theory approach is followed. The main results are applied to study a suitable notion of Hardy spaces.
Degree theory for VMO maps on metric spaces
We construct a degree theory for Vanishing Mean Oscillation functions in metric spaces, following some ideas of Brezis & Nirenberg. The underlying sets of our metric spaces are bounded open subsets of and their boundaries. Then, we apply our results in order to analyze the surjectivity properties of the -harmonic extensions of VMO vector-valued functions. The operators we are dealing with are second order linear differential operators sum of squares of vector fields satisfying the hypoellipticity...
Frequency functions on the Heisenberg group, the uncertainty principle and unique continuation
A recent result of Bahouri shows that continuation from an open set fails in general for solutions of where and is a (nonelliptic) operator in satisfying Hörmander’s condition for hypoellipticity. In this paper we study the model case when is the subelliptic Laplacian on the Heisenberg group and is a zero order term which is allowed to be unbounded. We provide a sufficient condition, involving a first order differential inequality, for nontrivial solutions of to have a finite order...
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.
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.
Subharmonic functions in sub-Riemannian settings
In this paper we furnish mean value characterizations for subharmonic functions related to linear second order partial differential operators with nonnegative characteristic form, possessing a well-behaved fundamental solution . These characterizations are based on suitable average operators on the level sets of . Asymptotic characterizations are also considered, extending classical results of Blaschke, Privaloff, Radó, Beckenbach, Reade and Saks. We analyze as well the notion of subharmonic function...
Commemorazione di Bruno Pini
On the smoothness of viscosity solutions of the prescribed Levi-curvature equation
In this paper a -regularity result for the strong viscosity solutions to the prescribed Levi-curvature equation is announced. As an application, starting from a result by Z. Slodkowski and G. Tomassini, the -solvability of the Dirichlet problem related to the same equation is showed.
Esistenza e unicità degli stati fondamentali per equazioni ellittiche quasilineari
In this paper we describe some existence and uniqueness theorems for radial ground states of a class of quasilinear elliptic equations. In particular, the mean curvature operator and the degenerate Laplace operator are considered.
Esistenza e unicità degli stati fondamentali per equazioni ellittiche quasilineari
In this paper we describe some existence and uniqueness theorems for radial ground states of a class of quasilinear elliptic equations. In particular, the mean curvature operator and the degenerate Laplace operator are considered.
Classical, viscosity and average solutions for PDE’s with nonnegative characteristic form
We compare several definitions of weak solutions to second order partial differential equations with nonnegative characteristic form.
Liouville theorems for a class of linear second-order operators with nonnegative characteristic form.
Levi's parametrix for some sub-elliptic non-divergence form operators.
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