Compactness and Subellipticity for the D-Bar Neumann Operator on Domains with Minimal Smoothness

Doctoral Dissertation

Abstract

In this thesis, we shall examine a strong form of Oka’s Lemma which provides sufficient conditions for compact and subelliptic estimates for the d-bar Neumann operator on Lipschitz domains. On smooth domains, the condition for subellipticity is equivalent to D'Angelo finite-type and the condition for compactness is equivalent to Catlin’s condition (P).

Once the basic properties of this condition have been established, we will study the extent to which these estimates can be extended to higher order derivatives on C^k domains, with k greater than or equal to 2. For the Lipschitz case, we will look at higher order estimates in the special case when the domain admits a plurisubharmonic defining function.

Finally, we will use these estimates to construct a compact solution operator for the boundary complex.

Attributes

Attribute NameValues
URN
  • etd-04132004-090527

Author Phillip S Harrington
Advisor Ikaros Bigi
Contributor Jianguo Cao, Committee Member
Contributor Alex Himonas, Committee Member
Contributor Nancy Stanton, Committee Member
Contributor Mei-Chi Shaw, Committee Member
Contributor Ikaros Bigi, Committee Chair
Degree Level Doctoral Dissertation
Degree Discipline Mathematics
Degree Name PhD
Defense Date
  • 2004-03-30

Submission Date 2004-04-13
Country
  • United States of America

Subject
  • non-coercive boundary value problems

  • partial differential equations

  • several complex variables

Publisher
  • University of Notre Dame

Language
  • English

Record Visibility Public
Content License
  • All rights reserved

Departments and Units

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