Mathematical Sciences: Theory of Capacities
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Work will be done investigating geometric-analytic                      properties of domains as they relate to solutions of partial                    differential equations.  The work concentrates on the boundaries                of domains for it is at the boundary where the nature of                        solutions tends to be obscure.  Among the concepts which have                   evolved in the measurement of boundary regularity, one of the                   most important is that of capacity, or more precisely, the                      capacity of a set.  Although there are a number of types of                     capacity one may define, the source of theory almost surely rests               with electrostatics and measurement of how well a conductor can                 support a charge.  This in itself is a question about solutions                 of a partial differential equations.                                                    Several questions in the theory of capacities will be                   addressed in this work.  The first is concerned with nature of                  weighted capacities arising in the study of degenerate elliptic                 equations.  One wishes to chacterize the boundary regular points                or the removable singularities for solutions.  The capacities                   (set functions) are built out of the differential operator.                     Certain fundamental questions as yet are incompletely answered.                 They include how weighted capacity depends on the weight at least               as far as null sets are concerned.  One would also want to be                   able to classify regular points into equivalence classes                        according to types of degeneracy.  On a larger scale, results on                equivalence of capacities and concepts of regularity for                        nonlinear equations are only just appearing.                                            This research will have application to the theory of partial            differential equations and potential theory.
{'FirstName': 'David', 'LastName': 'Adams', 'PI_MID_INIT': 'R', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'David R Adams', 'EmailAddress': 'dave@ms.uky.edu', 'NSF_ID': '000427808', 'StartDate': '08/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of Kentucky Research Foundation', 'CityName': 'LEXINGTON', 'ZipCode': '405260001', 'PhoneNumber': '8592579420', 'StreetAddress': '500 S LIMESTONE', 'StreetAddress2': '109 KINKEAD HALL', 'CountryName': 'United States', 'StateName': 'Kentucky', 'StateCode': 'KY', 'CONGRESSDISTRICT': '06', 'CONGRESS_DISTRICT_ORG': 'KY06', 'ORG_UEI_NUM': 'H1HYA8Z1NTM5', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF KENTUCKY RESEARCH FOUNDATION, THE', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '1261', 'Text': 'CLASSICAL ANALYSIS'}
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