# Higher regularity in congested traffic dynamics

*Verena BĂ¶gelein (University Salzburg, Austria)*

**16-Mar-2021, 18:00-19:00 (10 months ago)**

**Abstract: **We consider an elliptic system that is motivated by a congested traffic dynamics problem. It has the form
$$
\mathrm{div}\bigg((|Du|-1)_+^{p-1}\frac{Du}{|Du|}\bigg)=f,
$$
and falls into the context of very degenerate problems. Continuity properties of the gradient have been investigated in the scalar case by Santambrogio & Vespri and Colombo & Figalli.
In this talk we establish the optimal regularity of weak solutions in the vectorial case for any $p>1$. This is joint work with F. Duzaar, R. Giova and A. Passarelli di Napoli.

mathematical physicsanalysis of PDEsclassical analysis and ODEsdifferential geometryfunctional analysismetric geometrynumerical analysisoptimization and control

Audience: researchers in the topic

**Online Seminar "Geometric Analysis" **

**Series comments: **We discuss recent trends related to geometric analysis in a broad sense. The general idea is to solve geometric problems by means of advanced tools in analysis. We will include a wide range of topics such as geometric flows, curvature functionals, discrete differential geometry, and numerical simulation.

**Registration** and links to videos available at blatt.sbg.ac.at/onlineseminar.php

Organizers: | Simon Blatt*, Philipp Reiter*, Armin Schikorra*, Guofang Wang |

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