期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：1977
卷号：74
期号：6
页码：2214-2216
DOI：10.1073/pnas.74.6.2214
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：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.
关键词：partial differential equations ; several complex variables ; the δ-Neumann problem ; subelliptic a priori estimates ; ideals of germs of real analytic functions
