Irene Fonseca
Higher Order Variational Problems

ABSTRACT. Several questions in applied analysis motivated by issues in computer vision, physics, materials sciences and other areas of engineering may be treated as higher order variational problems. Their study often requires state-of-the-art techniques, new ideas, and the introduction of innovative tools in partial differential equations, geometric measure theory, and calculus of variations. In these lectures it will be shown how some of these questions may be reduced to well understood first order problems. Applications to phase transitions, foam drainage, micromagnetics and thin films will be addressed.