11/18/2004

Sylvia Serfaty
Courant Institute

A deterministic control based approach to motion by curvature

In a joint work with Bob Kohn, we give a new control-type interpretation on the level-set approach to motion by curvature and related interface motion laws. More precisely, we give a family of discrete-time, two-person games whose value functions converge in the continuous-time limit to the solution of the motion-by-curvature PDE. The value function of a deterministic control problem is normally a first-order Hamilton-Jacobi equation, while the level-set formulation of motion by curvature is a second-order parabolic equation.