Analysis and Probability Seminar

Abstract: This talk is about the energy-momentum equations in calculus of variations. These arises from inner variations, i.e., domain variations, as opposed to outer variations that give rise to the Euler-Lagrange equations. For minimisation problems involving vector valued functions the energy-momentum equations become important. In recent work I proved that the they are generically ill-posed with respect to Dirichlet data using convex integration theory. I also showed that they poses Lipschitz solutions that are nowhere continuously differentiable. A similar result for the Euler-Lagrange equations was proven by Müller and Several in 2003. Besides reporting on my work I will explain various fundamental notions for vectorial problems like quasiconvexity and rank-one convexity.