Some Novel Aspects of the Cauchy Problem

Abstract

We discuss two subtle Cauchy problems:

• 1. What happens to the Cauchy-Kowalewsky theorem when the initial data is not analytic? We show that there is a solution to the asymptotic Cauchy problem, meaning that Pf is not zero, but approaches 0 rapidly as we approach the Cauchy surface. The rapidity depends on the regularity of the initial data.

• 2. We introduce a new type of Cauchy problem. In particular, we show how it applies to the parametric Radon transform and gives a new insight into the sufficiency of the John equations.

To Carlos. It has been an honor to have you as my student.