Higher regularity in congested traffic dynamics

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