[CvGmt News] CVGMT: weekly bulletin

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Subject: CVGMT weekly bulletin

Weekly bulletin of http://cvgmt.sns.it/

--- Summary ---

* Seminars by: Colombo
* New papers by: Vittone, Scilla, Cavalletti, Magnani, Sobolevski, G?neysu, Tyson, Mariano, Modica, Giaquinta, Pallara, Huesmann, Khanin
* Modified papers by: Vittone, De Faveri, Goldman, Petrache, Freddi, Riviere, Roubicek, Dragoni, Paroni, Zanini, Nardulli, Barilari, Boscain, Rigot, Mondino, Brasco, Manfredi, Gigli, Neel, Paolini, Novaga, Leonardi, Monti

--- Seminars next week ---

* Wednesday 5 dec 2012
time: 17:00
Sala Seminari, Department od Mathematics, Pisa University

Regularity results for a very degenerate elliptic equation with applications to traffic dynamic
Maria Colombo (SNS Pisa)

Abstract. 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 $2$. As a corollary of our analysis, we recover the classical regularity for solutions of the $p$-Laplacian.

(joint work with Alessio Figalli)

--- New Papers ---

* Scilla: Variational problems with percolation: rigid spin system

* G?neysu, Pallara: Functions with bounded variation on a class of Riemannian manifolds with Ricci curvature unbounded from below

* Giaquinta, Mariano, Modica: Stress constraints in simple bodies undergoing large strains: a variational approach

* Magnani, Tyson, Vittone: On transversal submanifolds and their measure

* Cavalletti, Huesmann: Metric regularity for optimal transport plans

* Khanin, Sobolevski: On dynamics of Lagrangian trajectories for Hamilton-Jacobi equations

--- Modified Papers ---

* Paolini: Regularity for minimal boundaries in $R^n$ with mean curvature in $L^n$

* Goldman, Novaga: Volume-constrained minimizers for the prescribed curvature problem in periodic media

* Dragoni, Manfredi, Vittone: Weak Fubini Property and  infinity Harmonic Functions in Riemannian and Sub-Riemannian Manifolds

* Monti, Vittone: Sets with finite $\mathbb H$-perimeter and controlled normal

* Leonardi, Rigot, Vittone: Isodiametric sets in the Heisenberg group

* Freddi, Roubicek, Zanini: Quasistatic delamination of sandwich-like Kirchhoff-Love plates

* Barilari, Boscain, Neel: Small time heat kernel asymptotics at the sub-Riemannian cut locus

* De Faveri, Freddi, Paroni: No-tension bodies: a reinforcement problem

* Gigli, Mondino: A PDE approach to nonlinear potential theory in metric measure spaces

* Mondino, Riviere: Willmore Spheres in Compact Riemannian Manifolds

* Mondino, Riviere: Immersed Spheres of Finite Total Curvature into Manifolds

* Mondino, Nardulli: Existence of isoperimetric regions in non-compact Riemannian manifolds under Ricci or scalar curvature conditions

* Brasco, Petrache: A continuous model of transportation revisited

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