Mathematical Sciences: Harmonic Analysis and Partial        Differential 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}
Work on the project will continue research on the                          qualitative properties of solutions and solution operators of                   linear and nonlinear partial differential equations.  Emphases                  will be on linear elliptic and on nonlinear  evolution                          equations with minimal smoothness conditions.  By minimal                       smoothness conditions one means either conditions on the                        equation, on the domain or both.  From a practical point of                     view, information about solutions on nonsmooth domains is most                  often sought.  Only recently have certain boundary value                        problems of elliptic type defined on domains with boundaries,                   with edges and corners been completely resolved.  That is, one                  can predict the smoothness of the solutions at the boundary.                    Several important problems suggest themselves and will be the                   focus of work done on this project.  They include questions of                  extentions to the general elliptic equation, elliptic systems                   and higher order elliptic equations.  Some success has alresdy                  been achieved with fourth order equations.                                           While the elliptic equations on nonsmooth domains are                      beginning to be understood, the corresponding evolution                         equations (involving time derivatives) remains a mystery.  The                  ingredient missing is an inequality relating gradients with                     normal derivatives, usually classified as inequalities of                       Rellich type.  The best results to date depend on positivity of                 solutions of classical evolution equations.  Objectives in                      analyzing this class of solutions focus more on questions of                    long term behavior, boundedness and uniqueness.  Some                           computational approximations may be employed in these studies.
{'FirstName': 'Bjorn E.', 'LastName': 'Dahlberg', 'PI_MID_INIT': 'J', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Bjorn E. J Dahlberg', 'EmailAddress': None, 'NSF_ID': '000383252', 'StartDate': '05/01/1989', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Washington University', 'CityName': 'SAINT LOUIS', 'ZipCode': '63110', 'PhoneNumber': '3147474134', 'StreetAddress': 'ONE BROOKINGS DR', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Missouri', 'StateCode': 'MO', 'CONGRESSDISTRICT': '01', 'CONGRESS_DISTRICT_ORG': 'MO01', 'ORG_UEI_NUM': 'L6NFUM28LQM5', 'ORG_LGL_BUS_NAME': 'WASHINGTON UNIVERSITY, THE', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '1261', 'Text': 'CLASSICAL ANALYSIS'}
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