On the evolution governed by the infinity Laplacian

We review the basic properties of the degenerate and singular evolution equation $$u_t=\left(D2u\frac{Du}{\text{abs}Du}\right)\cdot \frac{Du}{\text{abs}Du},$$ which is a parabolic version of the increasingly popular infinity Laplace equation. We discuss how to obtain existence and uniqueness for both Dirichlet and Cauchy problems, establish interior and boundary Lipschitz estimates and a Harnack inequality, and also provide some interesting explicit solutions.

This is a joint work with Bernd Kawohl, Cologne.