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

这个项目将考虑部分理论中的问题， 拟正则映射的微分方程 维至少为3的欧几里德空间，试图扩展 更高维度的经典函数论的某些方面。 欧氏空间中的潜在理论是非线性的 和调和函数被某些解所代替 在一定意义下不变的拟线性方程 在拟正则映射下。 拟共形映射很好地 适合通过这些拟线性分析方法进行研究 椭圆方程他们是封闭的组成，使 它们在拓扑学和几何学中非常有用。 这些研究 在非牛顿流体的数学建模中很重要 和金属蠕变。 与适用福利的进一步联系 科学以及纯数学都将被探索。

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.