[CvGmt News] [Notiziario] [Settimanale] avviso seminario di matematica prof. Valentina Franceschi (21.01.2019)

[Valeria Giuliani]

SEMINARIO DI MATEMATICA



*Lunedì 21 gennaio 2019*

ore 14:00



*Scuola Normale Superiore*

Pisa

Aula Bianchi Scienze



*Valentina Franceschi*
(Université Paris Sud, Orasay, France)



Terrà un seminario dal titolo:

*“*On the essential self-adjointness of sub-Laplacians*”*



*Abstract:*

The aim of this seminar is to present some recent results on the  essential
self-adjointness of sub Laplacians. Given a smooth manifold M, a
sub-Laplacian is a hypoelliptic operator H, naturally associated to a
sub-Riemannian geometric structure and to a volume measure on it. If the
structure is Riemannian and complete, the associated Laplace-Beltrami
operator (in this case the volume is the intrinsic Riemannian measure) is
essentially self-adjoint. This amounts to say that the solutions to the
Schrodinger equation on M are well defined without imposing any boundary
conditions. If the structure is sub-Riemannian, sub-Laplacians are also
essentially self-adjoint, assuming completeness of the metric structure and
smoothnessn of the volume measure. In this seminar, we address the case
where the structure is sub-Riemannian and (1) either the measure (chosen to
be intrinsic) is non-smooth, (2) or the metric structure is
non-complete. Regarding
(1), we present results concerning sub-Riemannian structures endowed with
singular measures. A standing conjecture, formulated by Boscain and Laurent
asserts that singular sub-Laplacians are essentially self-adjoint out of
the singularity. We will explain our results supporting the conjecture and
underline the cases that are not included in our analysis. Regarding (2),
we present recent results on 3D sub-Laplacians defined on non-complete
sub-Riemannian manifolds, obtained by removing a point from a complete one.
We show that, unlike the 3D Euclidean case, essentially self-adjointness
holds in this setting.

This is a joint work with R.~Adami, U.~Boscain and D.~Prandi.



Tutti gli interessati sono invitati a partecipare.

Classe di Scienze


Valeria Giuliani
Scuola Normale Superiore
Servizio alla Didattica e Allievi
tel. 050 509260
Piazza dei Cavalieri, 7
56126 Pisa
E-mail: valeria.giuliani at sns.it
E-mail: classi at sns.it

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