Speaker: Craig Evans

Title: Calculus of variations in the sup norm

Abstract: In this series of three lectures I will discuss how to extend the conventional calculus of variations to a "calculus of variations in the sup-norm", and I will explain why it is interesting to do so.

In particular we will see that the conventional Euler-Lagrange equations transform into fascinating new sorts of PDE that characterize "absolute minimizers" for sup-norm energies. These new equations are nonlinear, second-order and elliptic, but are so degenerate that they behave somewhat like first-order PDE and in particular have "characteristics"

Lecture 1: Overview of sup-norm variational problems

Lecture 2: Fine properties of infinitely harmonic functions

Lecture 3: Other energies, Aronsson's equation