Schrödinger equation on the Heisenberg group
Solvability of invariant sublaplacians on spheres and group contractions
In the first part of this paper we study the local and global solvability and the hypoellipticity of a family of left-invariant sublaplacians on the spheres . In the second part, we introduce a larger family of left-invariant sublaplacians on and study the corresponding properties by means of a Lie group contraction to the Heisenberg group.
Some Examples of Hypoelliptic Partial Differential Equations.
Some Hardy type inequalities in the Heisenberg group.
Sous-ellipticité et hypoellipticité maximale pour des systèmes différentiels
Square roots of perturbed subelliptic operators on Lie groups
We solve the Kato square root problem for bounded measurable perturbations of subelliptic operators on connected Lie groups. The subelliptic operators are divergence form operators with complex bounded coefficients, which may have lower order terms. In this general setting we deduce inhomogeneous estimates. In case the group is nilpotent and the subelliptic operator is pure second order, we prove stronger homogeneous estimates. Furthermore, we prove Lipschitz stability of the estimates under small...
Stability of mappings with bounded distortion in the Sobolev norm on the John domains of Heisenberg groups.
Stochastic calculus and degenerate boundary value problems
Consider the boundary value problem (L.P): in , on where is written as , and is a general Venttsel’s condition (including the oblique derivative condition). We prove existence, uniqueness and smoothness of the solution of (L.P) under the Hörmander’s condition on the Lie brackets of the vector fields (), for regular open sets with a non-characteristic boundary.Our study lies on the stochastic representation of and uses the stochastic calculus of variations for the -diffusion process...
Su una classe di operatori differenziali ipoellittici del second’ordine
Subelliptic Poincaré inequalities: the case p < 1.
We obtain (weighted) Poincaré type inequalities for vector fields satisfying the Hörmander condition for p < 1 under some assumptions on the subelliptic gradient of the function. Such inequalities hold on Boman domains associated with the underlying Carnot- Carathéodory metric. In particular, they remain true for solutions to certain classes of subelliptic equations. Our results complement the earlier results in these directions for p ≥ 1.
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...
Sul comportamento degli operatori differenziali ipoellittici, a coefficienti costanti, sopra i «wave front sets»
Sulle soluzioni delle equazioni differenziali lineari ellittiche e con coefficienti analitici
Sur l'hypoellipticité des opérateurs pseudodifférentiels à caractéristiques multiples (perte de 3/2 dérivées)
Sur une classe d'opérateurs différentiels hypoelliptiques à coefficients analytiques
Sur une classe d'opérateurs partiellement hypoelliptiques
Sur une classe d'opérateurs pseudodifférentiels hypoelliptiques à caractéristiques doubles, d'après L. Hörmander