THE DIRICHLET PROBLEM FOR SUPERDEGENERATE DIFFERENTIAL OPERATORS

DENIS R. BELL SALAH E.-A. MOHAMMED

Abstract. Let L be an infinitely degenerate second-order linear operator defined on a bounded smooth Euclidean domain. Under weaker conditions than those of Hörmander, we show that the Dirichlet problem associated with L has a unique smooth classical solution. The proof uses the Malliavin calculus. At present, there appears to be no proof of this result using classical analytic techniques.