This project will consider problems in the theory of partial differential equations related to quasiregular mappings in Euclidean space of dimension at least 3, in an attempt to extend to higher dimensions some aspects of classical function theory. The underlying potential theory in Euclidean space is nonlinear and harmonic functions are replaced by solutions of certain quasilinear equations which are invariant in a certain sense under quasiregular mappings. Quasiconformal mappings are well suited to be studied with analytic methods via these quasilinear elliptic equations. They are closed under composition, making them very useful in Topology and Geometry. These studies are important in the mathematical modelling of non-newtonian fluids and creep of metals. Further connections to benefit applied science as well as pure mathematics will be sought.

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Application #
9101864
Program Officer
John V. Ryff
Project Start
Project End
Budget Start
1991-06-01
Budget End
1994-11-30
Support Year
Fiscal Year
1991
Total Cost
$61,725
Indirect Cost
Name
University of Pittsburgh
Department
Type
DUNS #
City
Pittsburgh
State
PA
Country
United States
Zip Code
15213