Speaker: Paul Woon Yin Lee
UC Berkeley

Title: Continuity of Optimal Control Costs and its application to
Weak KAM Theory

Abstract: The weak KAM theorem states that the stationary Hamilton-Jacobi
equation H(x,Df_x)=constant has a kind of weak solution called viscosity
solution. In this talk, we will discuss a version of weak KAM theorem
corresponding to a family optimal control problems. The proof of such
theorem relies on the continuity of the corresponding optimal control
cost. I will give conditions which guarantees this continuity and show
that the condition is sharp. This is a joint work with A. Agrachev.