Mathematical Sciences: Free Boundary Problems, Fully        Nonlinear Equations, Nonlinear Parabolic Equations and the  Navier-Stokes Equations
{'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 project will cover problems in nonlinear partial                       differential equations.  On free boundary problems, new methods                 are being developed to study the regularity of free boundaries.                 Work will be done in establishing "Harnack"-type inequalities                   for free boundaries along the lines of the corresponding                        inequalities for linear equations with bounded measurable                       coefficients by De Giorgi and Krylov.  Plans are to study two-                  phase Stefan problems and minimal surface problems as well.                          Work will also continue on fully nonlinear equations.  A                   main constraint in the theory is the concavity of the nonlinear                 function in its dependence on the second derivatives of the                     unknown function.  Plans are to investigate where the                           coefficients are not necessarily continuous. Efforts will be made               to get optimal regularity and uniqueness theorems.  The                         regularity of solutions of nonlinear systems of parabolic                       equations will be investigated.  In addition, work will be done                 on Navier Stokes equations in three space dimensions.  The                      earlier work with Kohn and Nirenberg suggests that the known                    solution should be in weak Lebesgue Space.  This will be explored               along with the possible construction of singular solutions.
{'FirstName': 'Luis', 'LastName': 'Caffarelli', 'PI_MID_INIT': 'A', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Luis A Caffarelli', 'EmailAddress': 'caffarel@math.utexas.edu', 'NSF_ID': '000387147', 'StartDate': '08/15/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Institute For Advanced Study', 'CityName': 'PRINCETON', 'ZipCode': '085404952', 'PhoneNumber': '6097348000', 'StreetAddress': '1 EINSTEIN DR', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'New Jersey', 'StateCode': 'NJ', 'CONGRESSDISTRICT': '12', 'CONGRESS_DISTRICT_ORG': 'NJ12', 'ORG_UEI_NUM': 'MNMJWSC5Z4H1', 'ORG_LGL_BUS_NAME': 'INSTITUTE FOR ADVANCED STUDY - LOUIS BAMBERGER & MRS FELIX FULD FOUNDATION', 'ORG_PRNT_UEI_NUM': None}
{'Name': None, 'CityName': None, 'StateCode': None, 'ZipCode': None, 'StreetAddress': None, 'CountryCode': None, 'CountryName': None, 'StateName': None, 'CountryFlag': None, 'CONGRESSDISTRICT': None, 'CONGRESS_DISTRICT_PERF': '""'}
{'Code': '1261', 'Text': 'CLASSICAL ANALYSIS'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1987&All=true', 'xml': '8718193.xml'}