Variational Methods in Materials and Imaging Problems

Irene Fonseca
Carnegie Mellon University

Abstract: Several questions in applied analysis motivated by issues in computer vision, physics, materials sciences and other areas of engineering may be treated variationally leading to higher order problems and to models involving lower dimension density measures. 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 the calculus of variations. Applications to the equilibrium of foams under the action of surfactants, imaging, micromagnetics and thin films will be addressed.