[CvGmt News] Seminario Lorenzo Giacomelli (18/10/2016)

[Alfonso Sorrentino]

SEMINARIO DI ANALISI DI EQUAZIONI DIFFERENZIALI
Dipartimento di Matematica
Universita' degli Studi di Roma "Tor Vergata"


Martedi' 18 Ottobre 2016, ore 14:30 Aula dal Passo


Lorenzo Giacomelli (Sapienza, Universita' di Roma)


Titolo: The 1-harmonic flow

Abstract: The 1-harmonic flow is the formal gradient flow -- with respect
to the $L^2$-distance -- of the total variation of a manifold-valued
unknown function. The problem originates from image processing and has an
intrinsic analytical interest as prototype of constrained and
vector-valued evolution equations in BV-spaces. For the resulting PDE, I
will introduce a notion of solution and I will discuss existence and
uniqueness results for two specific manifolds: the hyper-octant of an
N-dimensional sphere and a connected sub-arc of a regular Jordan curve. I
will also present possible extensions to general manifolds, together with
related open questions and conjectures.
Based on joint works with Agnese Di Castro, José Mazòn, and Salvador Moll.




Website: http://www.mat.uniroma2.it/~sorrenti/SeminarioED.html