Mathematical Sciences: Partial Regularity in the Calculus ofVariations
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{'SignBlockName': 'John V. Ryff', 'PO_EMAI': None, 'PO_PHON': None}
Work is planned on problems in the calculus of variations.                 Specifically, the principal investigator is concerned with the                  regularity and existence of minimizers of integral functions                    whose integrands exhibit a certain type of singular behavior.                   Fundamental to existence theory is a result of C.B. Morrey which                isolates the notion of quasiconvexity as an essential ingredient                for existence.  A stronger property formulated by L.C. Evans                    called strict quasiconvexity guarantees partial regularity of                   minimizers.                                                                          It has been pointed out in recent literature that in studies               of equilibrium boundary value problems in nonlinear elasticity                  that the growth conditions required to guarantee regularity is                  too restrictive to include realistic models for hyperelastic                    materials where the functional being minimized (i.e. its                        integral) corresponds to stored energy.  This problem occurs in                 particular when one is dealing with compressible materials.                          Work will be done with integrands exhibiting unboundedness,                subject only to the restriction that the determinant of the                     gradient of admissible functions (representing hydrostatic                      pressure) be positive.  Existence of minimizers is not a problem                in this context but regularity is.  The variational problem                     yields an Euler equation but it is not at all clear that a                      minimizer is even a weak solution of this equation.  Work to date               suggests nevertheless that a careful analysis of admissible                     variations will yield the desired regularity.                                        This research is expected to find applications in the study                of nonlinear elasticity and incompressible fluid flow.
{'FirstName': 'Ronald', 'LastName': 'Gariepy', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Ronald Gariepy', 'EmailAddress': 'gariepy@ms.uky.edu', 'NSF_ID': '000318016', 'StartDate': '07/15/1987', '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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