Mathematical Sciences: Singularities of Harmonic Function inCn
{'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}
The main theme of this work, to investigate the holomorphic                continuation of solutions of holomorphic partial differential                   equations in domains within the space of several real or complex                varibles, will employ techniques from three areas of mathematical               analysis.  They are partial differential equations, complex                     analysis and potential theory.                                                       The extent to which solutions of elliptic equations extend                 from hypersurfaces to surrounding domains is believed to be                     directly related to the maximum extension of the Schwarz                        potential.  It should be mentioned that the question of maximal                 extent of solutions of equations of hyperbolic type (wave                       equations) has been thoroughly investigated.  In the case of                    equations of elliptic type, such as Laplace's equation,                         conjectures of what the maximal extent should be have not even                  been formulated.  Present work will focus on very specific                      questions regarding homogeneous equations with holomorphic                      boundary values.  The first objective will be to determine                      whether or not the maximal domain of analyticity of a                           solution depends only on the differential operator and the                      boundary, but not the specific Cauchy data.  A simple device                    which has proved valuable in the cases of equations in two real                 dimensions is the Schwarz function of an analytic curve.  The                   domain of regularity of the Schwarz function plays a crucial role               in determining the maximal region of analyticity for  solutions                 of elliptic initial value problems with analytic data.                               A reasonable extension of the Schwarz function has been                    formulated which will be examined to determine whether the basic                two-dimensional results can be expanded to higher real dimensions               and (any) complex ones.  Preliminary analysis will be done on                   problems where the Cauchy data consists of polynomials, with                    later goals to include entire functions.
{'FirstName': 'Dmitry', 'LastName': 'Khavinson', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Dmitry Khavinson', 'EmailAddress': 'dkhavins@usf.edu', 'NSF_ID': '000103194', 'StartDate': '06/01/1989', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of Arkansas', 'CityName': 'FAYETTEVILLE', 'ZipCode': '727013124', 'PhoneNumber': '4795753845', 'StreetAddress': '1125 W MAPLE ST STE 316', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Arkansas', 'StateCode': 'AR', 'CONGRESSDISTRICT': '03', 'CONGRESS_DISTRICT_ORG': 'AR03', 'ORG_UEI_NUM': 'MECEHTM8DB17', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF ARKANSAS', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '1261', 'Text': 'CLASSICAL ANALYSIS'}
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