Mathematical Sciences: The Degree of Regularity of          Quasiregular Mapping and Minima of Related NondifferentiableFunctions in the Calculus of Variations
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{'SignBlockName': 'John V. Ryff', 'PO_EMAI': None, 'PO_PHON': None}
Work to be carried out on this project will focus on                       quasiconformal and quasiregular mapping of Euclidean space.                     These mappings - (the distinction being that quasiconformal maps                are univalent) - arise in a number of analytical and geometric                  contexts.  They play important roles in our understanding of                    classes of partial differential equations.  The problems to be                  investigated are closely related, motivated by both theoretical                 interest as well as by their applicability to regularity theory                 for elliptic equations and estimates of singular integrals.                          Quasiregular mappings are known to be solutions of n-                      dimensional Beltrami systems of partial differential equations,                 which may have discontinuous terms.  One of the objectives of                   this work will be to find minimizers for the total energy among                 suitable classes of these mappings.  The variational problems                   associated with this minimization arise in nonlinear                            elastostatics.                                                                       It has been recognized that the correct way of measuring the               degree of regularity of a quasiregular mapping as well as                       studying the mimima of non-differentiable functionals is through                the Holder exponent or by the exponent of integrability of their                derivatives.  A second objective of this work will be to identify               the best exponents or at least describe the quantitative                        character of the allowable exponents.  Related work will seek to                find sharp estimates for two-dimensional Hilbert transforms and                 to examine the asymptotic behavior of the power norms of the                    transform.
{'FirstName': 'Tadeusz', 'LastName': 'Iwaniec', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Tadeusz Iwaniec', 'EmailAddress': 'tiwaniec@mailbox.syr.edu', 'NSF_ID': '000328599', 'StartDate': '07/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
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{'Code': '126100', 'Text': 'CLASSICAL ANALYSIS'}
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