Sufficient conditions for subellipticity on weakly pseudo-convex domains.
Herein is outlined a method for studying a priori estimates by using the theory of ideals of functions. With this method a criterion is obtained for subelliptic estimates for the delta-Neumann problem. In case the boundary is real analytic, the theory of ideals of real-analytic functions gives a geometric interpretation of the criterion. For forms of type (p,n - 1), in which n is the complex dimension of the domain, we obtain necessary and sufficient conditions for subellipticity on pseudo-convex domains. The study of propagation of singularities for delta leads one to conjecture that, for pseudo-convex domains, with real-analytic boundaries, subellipticity for (p,q)-forms holds if and only if there are no complex-analytic varieties of dimension greater than or equal to q in the boundary. The methods described here give results concerning the sufficiency of the condition in this conjecture.
Kohn
J J
JJ
Department of Mathematics, Princeton University, Princeton, New Jersey 08540.