Sufficient conditions for subellipticity on weakly pseudo-convex domains
- 1 June 1977
- journal article
- Published by Proceedings of the National Academy of Sciences in Proceedings of the National Academy of Sciences
- Vol. 74 (6) , 2214-2216
- https://doi.org/10.1073/pnas.74.6.2214
Abstract
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.Keywords
This publication has 1 reference indexed in Scilit:
- Exhaustion functions and Stein neighborhoods for smooth pseudoconvex domainsProceedings of the National Academy of Sciences, 1975