Mathematical Sciences: Partial Differential Equations and   Classical 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}
This project will focus primarily on problems arising in the               theory of elliptic partial differential equations.  They are                    motivated to some extent by considerations of quasiregular                      mappings in n-dimensional Euclidean space.  These are considered                as natural extensions to higher dimension of classical analytic                 function theory.  In addition, solutions of quasilinear elliptic                partial differential equations replace harmonic functions.  The                 conformally invariant extension to n-dimensions of the Laplace                  operator is the so-called N-Laplacian.                                               Work will be done in seeking conditions on bounded weak                    solutions of quasilinear equations to have gradients of bounded                 mean oscillation.  Even in the linear case this question is still               open.  Estimates on the oscillation of boundary values of the                   gradient will be sought.                                                             Another line of investigation will focus on the existence of               branched quasiregular maps.  When the maps are sufficiently                     smooth, no branching occurs.  The minimal smoothness assumptions                are not known.                                                                       Finally, studies will be made of parabolic divergence type                 equations to establish whether Holder continuity can be expected                of bounded weak solutions.                                                           This work is related to research in conformal geometry and                 potential theory.
{'FirstName': 'Juan', 'LastName': 'Manfredi', 'PI_MID_INIT': 'J', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Juan J Manfredi', 'EmailAddress': 'manfredi@pitt.edu', 'NSF_ID': '000394692', 'StartDate': '07/15/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Purdue University', 'CityName': 'WEST LAFAYETTE', 'ZipCode': '479061332', 'PhoneNumber': '7654941055', 'StreetAddress': '2550 NORTHWESTERN AVE # 1100', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Indiana', 'StateCode': 'IN', 'CONGRESSDISTRICT': '04', 'CONGRESS_DISTRICT_ORG': 'IN04', 'ORG_UEI_NUM': 'YRXVL4JYCEF5', 'ORG_LGL_BUS_NAME': 'PURDUE UNIVERSITY', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '1261', 'Text': 'CLASSICAL ANALYSIS'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1987&All=true', 'xml': '8703286.xml'}