[CvGmt News] Colloquium di Dipartimento - Albert Fathi (29 maggio ore 16)

[Alfonso Sorrentino]

COLLOQUIUM DI DIPARTIMENTO


Mercoledì 29 Maggio 2019 - h. 16:00
Dipartimento di Matematica, Università di Roma "Tor Vergata"

Aula "Roberta Dal Passo"


Speaker: Prof. Albert Fathi (Georgia Institute of Technology, USA)
Title:    "Singularities of solutions of the Hamilton-Jacobi equation. A
toy model: distance to a closed subset "

Abstract:   This is a joint work with Piermarco Cannarsa and Wei Cheng. The
distance function $d_F$ to a closed subset $F$ of Euclidean space ${ f
R}^k$ is given by $$d_F(x)=inf_{fin F}|x-f|.$$ It is a Lipschitz, hence
differentiable almost everywhere. We will discuss some topological
properties of the set ${ m Sing}(d_F)$ of points where $d_F$ is not
differentiable. More generally, we will discuss properties of the set of
singularities of a viscosity solution of the Hamilton-Jacobi equation
$$partial_tU+H(x,partial_xU)=0,$$ when $H$ is a Tonelli Hamiltonian. We
will give applications in Riemannian geometry. We will explain during the
lecture all notions (beyond common knowledge) necessary to understand it.

N.B.: This talk is part of the activity of the MIUR Excellence Department
Project MATH at TOV CUP E83C18000100006













*-  At the end of the Colloquium, there will be a refreshment ---
Dipartimento di MatematicaUniversità degli Studi di Roma "Tor Vergata"Via
della Ricerca Scientifica 100133 Rome (Italy)Phone: +39 06 72594663Fax:
 +39 06 72594699Web page: http://www.mat.uniroma2.it/~sorrenti
<http://www.mat.uniroma2.it/~sorrenti>Email: sorrentino at mat.uniroma2.it
<sorrentino at mat.uniroma2.it>*
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