Mathematical Sciences: Partial Differential Equations in    Complex Analysis
{'Code': '03040102', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'John V. Ryff', 'PO_EMAI': None, 'PO_PHON': None}
Work planned on this project centers on a single broad                     question: isolate the local and global boundary regularity                      properties of partial differential operators on domains in                      complex n-dimensional space.  The research combines analytic                    methods of differential equations with geometric concepts in                    several complex variables.  The focus will be on differential                   operators which play a natural role in the study of holomorphic                 functions, the so-called d-bar and box-b operators.  Aside from                 intrinsic interest, the research has its roots in a fundamental                 discovery of Charles Fefferman in the 1970's that biholomorphic                 mappings between certain domains (pseudoconvex) have natural and                continuous extensions to the respective boundaries.  To achieve                 this, an integral transform, the Bergman operator must be shown                 to be analytic on the boundary of each domain.                                       This research seeks to expand the results to a much larger                 class of domains known as weakly pseudoconvex.  One must begin                  with the case of domains with real analytic boundaries.  The                    necessary estimates have been obtained to yield positive results                in the case of certain weakly pseudoconvex domains, in particular               domains embedded in larger, biholomorphic domains can be treated.               New local results suggest that global analytic regularity up to                 the boundary is true and accessible.  Work will concentrate on                  those domains which are nonembeddable, for if the conjecture                    fails, it must do so in one of these circumstances.                                  Applications of this work are planned in the general                       classification of domains and in the development of a priori                    estimates of solutions of partial differential equations.
{'FirstName': 'David', 'LastName': 'Tartakoff', 'PI_MID_INIT': 'S', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'David S Tartakoff', 'EmailAddress': 'dst@uic.edu', 'NSF_ID': '000104293', 'StartDate': '06/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of Illinois at Chicago', 'CityName': 'CHICAGO', 'ZipCode': '606124305', 'PhoneNumber': '3129962862', 'StreetAddress': '809 S MARSHFIELD AVE M/C 551', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Illinois', 'StateCode': 'IL', 'CONGRESSDISTRICT': '07', 'CONGRESS_DISTRICT_ORG': 'IL07', 'ORG_UEI_NUM': 'W8XEAJDKMXH3', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF ILLINOIS', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '126100', 'Text': 'CLASSICAL ANALYSIS'}
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