Speaker: Wilfrid Gangbo, University of California, Los Angeles

Title: A weaker notion of convexity for Lagrangians not depending solely on velocities and positions

Date: 03/21/2019

Time: 4:10 PM - 5:00 PM

Place: C304 Wells Hall

In dynamical systems, one often encounters actions $\mathcal{A}\equiv \int_{\Omega}L(x, v(x))\rho dx$ which depend only on $v$, the velocity of the system and on $\rho$ the distribution of the particles. In this case, it is well–understood that convexity of $L(x, \cdot)$ is the right notion to study variational problems. In this talk, we consider a weaker notion of convexity which seems appropriate when the action depends on other quantities such as electro–magnetic fields. Thanks to the introduction of a gauge, we will argue why our problem reduces to understanding the relaxation of a functional defined on the set of differential forms (Joint work with B. Dacorogna).