Formation of small scales in nonlinear PDEs

Variational methods for hypoelliptic equations

Scott Armstrong

New York University

We present a functional analytic approach to the linear kinetic Fokker-Planck equation which mimics the H^1 theory for uniformly elliptic equations. Using a new Poincare inequality, we are able to develop a well-posedness and regularity theory for weak solutions and give a simplified proof of exponential decay to equilibrium. We also give the equation a variational interpretation by showing that weak solutions are minimizers of a uniformly coercive energy functional.