Mathematical Sciences: Partial Differental Equations and Systems Related to Quasiregular Mappings

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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.