Applied Variational Analysis
This course will discuss a handful of topics from the modern calculus of variations, concerning the study of minimizers or lack thereof for a given energy functional on an infinite dimensional space. We will discuss the interplay between convexity, coercivity and existence of minimizers, as well as the many consequences of non-convexity for non-existence and relaxation phenomena. Other topics may include optimal transport theory, homogenization, singular perturbation and/or variational limits (Gamma-convergence) as time permits. Much of our discussion will be motivated by physical modeling, though a background in physics or engineering is not required. Some exposure to Sobolev spaces would be helpful, but is also not required. We will briefly review the necessary measure-theoretic machinery when it arises.
TBA
See course description.