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<h1>CVGMT Weekly Bulletin</h1>
<h2>Summary</h2>
<p><b>Seminars by:</b> <a href='/seminar/304/'>Colombo</a></p>
<p><b>New papers by:</b> <a href='/person/256/' >Vittone</a>, <a href='/person/1217/' >Scilla</a>, <a href='/person/27/' >Cavalletti</a>, <a href='/person/228/' >Magnani</a>, <a href='/person/167/' >Sobolevski</a>, <a >Güneysu</a>, <a >Tyson</a>, <a >Mariano</a>, <a href='/person/187/' >Modica</a>, <a href='/person/92/' >Giaquinta</a>, <a href='/person/157/' >Pallara</a>, <a >Huesmann</a>, <a >Khanin</a></p>
<p><b>Modified papers by:</b> <a href='/person/256/'>Vittone</a>, <a >De Faveri</a>, <a href='/person/260/'>Goldman</a>, <a href='/person/136/'>Petrache</a>, <a href='/person/139/'>Freddi</a>, <a >Riviere</a>, <a >Roubicek</a>, <a href='/person/162/'>Dragoni</a>, <a >Paroni</a>, <a href='/person/45/'>Zanini</a>, <a href='/person/177/'>Nardulli</a>, <a href='/person/1084/'>Barilari</a>, <a >Boscain</a>, <a >Rigot</a>, <a href='/person/965/'>Mondino</a>, <a href='/person/198/'>Brasco</a>, <a href='/person/93/'>Manfredi</a>, <a href='/person/226/'>Gigli</a>, <a >Neel</a>, <a href='/person/117/'>Paolini</a>, <a href='/person/119/'>Novaga</a>, <a href='/person/254/'>Leonardi</a>, <a href='/person/127/'>Monti</a></p>
<p><b>Open positions:</b> <a href='/position/58/'>Post-doc and Ph.D. positions with A. Pratelli in Erlangen</a>; <a href='/position/55/'>Lecturer Pure Mathematics, University of Bristol</a>; <a href='/position/54/'>Scientific Director of the Basque Center for Applied Mathematics, Bilbao</a>; <a href='/position/57/'>3 year PhD Position in Muenster (Germany) </a></p>
<h2>Seminars next week</h2>
<p><i>Wednesday 5 dec 2012</i></p>
<p>
time: 17:00<br />
Sala Seminari, Department od Mathematics, Pisa University<br/>
<b><a href='/seminar/304/'>Regularity results for a very degenerate elliptic equation with applications to traffic dynamic</a></b><br />
Maria Colombo (SNS Pisa)<br />
<b>Abstract.</b> <p>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.
</p>
<p>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.
</p>
<p>(joint work with Alessio Figalli)</p>
<br />
<h2>New Papers</h2>
<p><b> Scilla:</b> <a href='/paper/2043/'>Variational problems with percolation: rigid spin system</a></p>
<p><b> Güneysu, Pallara:</b> <a href='/paper/2044/'>Functions with bounded variation on a class of Riemannian manifolds with Ricci curvature unbounded from below</a></p>
<p><b> Giaquinta, Mariano, Modica:</b> <a href='/paper/2045/'>Stress constraints in simple bodies undergoing large strains: a variational approach</a></p>
<p><b> Magnani, Tyson, Vittone:</b> <a href='/paper/2046/'>On transversal submanifolds and their measure</a></p>
<p><b> Cavalletti, Huesmann:</b> <a href='/paper/2047/'>Metric regularity for optimal transport plans</a></p>
<p><b> Khanin, Sobolevski:</b> <a href='/paper/2048/'>On dynamics of Lagrangian trajectories for Hamilton-Jacobi equations</a></p>
<h2>Modified Papers</h2>
<p><b> Paolini:</b> <a href='/paper/232/'>Regularity for minimal boundaries in $R^n$ with mean curvature in $L^n$</a></p>
<p><b> Goldman, Novaga:</b> <a href='/paper/497/'>Volume-constrained minimizers for the prescribed curvature problem in periodic media</a></p>
<p><b> Dragoni, Manfredi, Vittone:</b> <a href='/paper/600/'>Weak Fubini Property and infinity Harmonic Functions in Riemannian and Sub-Riemannian Manifolds</a></p>
<p><b> Monti, Vittone:</b> <a href='/paper/656/'>Sets with finite $\mathbb H$-perimeter and controlled normal</a></p>
<p><b> Leonardi, Rigot, Vittone:</b> <a href='/paper/866/'>Isodiametric sets in the Heisenberg group</a></p>
<p><b> Freddi, Roubicek, Zanini:</b> <a href='/paper/1808/'>Quasistatic delamination of sandwich-like Kirchhoff-Love plates</a></p>
<p><b> Barilari, Boscain, Neel:</b> <a href='/paper/1823/'>Small time heat kernel asymptotics at the sub-Riemannian cut locus</a></p>
<p><b> De Faveri, Freddi, Paroni:</b> <a href='/paper/1861/'>No-tension bodies: a reinforcement problem</a></p>
<p><b> Gigli, Mondino:</b> <a href='/paper/1919/'>A PDE approach to nonlinear potential theory in metric measure spaces</a></p>
<p><b> Mondino, Riviere:</b> <a href='/paper/1920/'>Willmore Spheres in Compact Riemannian Manifolds</a></p>
<p><b> Mondino, Riviere:</b> <a href='/paper/1921/'>Immersed Spheres of Finite Total Curvature into Manifolds</a></p>
<p><b> Mondino, Nardulli:</b> <a href='/paper/1977/'>Existence of isoperimetric regions in non-compact Riemannian manifolds under Ricci or scalar curvature conditions</a></p>
<p><b> Brasco, Petrache:</b> <a href='/paper/2013/'>A continuous model of transportation revisited</a></p>
<h2>Open Positions</h2>
<p> <a href="/position/58/">Post-doc and Ph.D. positions with A. Pratelli in Erlangen</a> (deadline: 1 Dec 2012) </p>
<p> <a href="/position/55/">Lecturer Pure Mathematics, University of Bristol</a> (deadline: 10 Dec 2012) </p>
<p> <a href="/position/54/">Scientific Director of the Basque Center for Applied Mathematics, Bilbao</a> (deadline: 31 Dec 2012) </p>
<p> <a href="/position/57/">3 year PhD Position in Muenster (Germany) </a> (deadline: 31 Mar 2013) </p>
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