Monday, May 20, 2019 - 3:30pm
In fluid mechanics, one deals with actions int(L) which depend only on the momentum m and distribution rho of the system of the particles. In this case, it is well-understood that convexity of L is the right notion for studying variational problems. Following a theory by C Morrey in 1966, we propose a weaker notion of convexity, appropriate for actions depending on other quantities such as electromagnetic fields. We introduce a gauge which reduces our problem to understanding the relaxation of a functional defined on the set of k-differential forms (Joint work with B. Dacorogna).