Colombo: Regularity results for a very degenerate elliptic equation with applications to traffic dynamic

We consider the equation
$$\nabla \cdot (\nabla F(\nabla u)) = f,$$
where $F:{\mathbb R}^n\to{\mathbb R}$ is a convex function. We are interested in the regularity of solutions in the case of a strongly degenerate $F$. In particular, we consider a function $F$ which is $0$ inside some convex set $E$ and is uniformly elliptic outside $E$. The particular choice of $F$ arises in the context of traffic congestion. Under some natural assumptions on $F$ and $f$, we prove that the function $\nabla F(\nabla u)$ is continuous in any dimension, extending a previous result by Santambrogio and Vespri valid only in dimension $2$.
(joint work with Alessio Figalli)
http://cvgmt.sns.it/seminar/304/
            

When	Wed Dec 5, 2012 4pm – 5pm Coordinated Universal Time
Where	Sala Seminari, Department od Mathematics, Pisa University (map)