On the evolution governed by the infinity Laplacian

We review the basic properties of the degenerate and singular evolution equation \[ u_t=\left(D2 u \frac{Du}{\abs{Du}}\right)\cdot\frac{Du}{\abs{Du}}, \] 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.