## Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

## If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

# Subellipticity of the $\overline\partial$-Neumann Problem on Nonpseudoconvex Domains

Lop-Hing Ho
Transactions of the American Mathematical Society
Vol. 291, No. 1 (Sep., 1985), pp. 43-73
DOI: 10.2307/1999894
Stable URL: http://www.jstor.org/stable/1999894
Page Count: 31
Preview not available

## Abstract

Following the work of Kohn, we give a sufficient condition for subellipticity of the $\overline\partial$-Neumann problem for not necessarily pseudoconvex domains. We define a sequence of ideals of germs and show that if 1 is in any of them, then there is a subelliptic estimate. In particular, we prove subellipticity under some specific conditions for n - 1 forms and for the case when the Levi-form is diagonalizable. For the necessary conditions, we use another method to prove that there is no subelliptic estimate for q forms if the Leviform has n - q - 1 positive eigenvalues and q negative eigenvalues. This was proved by Derridj. Using similar techniques, we prove a necessary condition for subellipticity for some special domains. Finally, we give a remark to Catlin's theorem concerning the hypoellipticity of the $\overline\partial$-Neumann problem in the case of nonpseudoconvex domains.

• 43
• 44
• 45
• 46
• 47
• 48
• 49
• 50
• 51
• 52
• 53
• 54
• 55
• 56
• 57
• 58
• 59
• 60
• 61
• 62
• 63
• 64
• 65
• 66
• 67
• 68
• 69
• 70
• 71
• 72
• 73