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

数学科学：偏微分方程和与拟正则映射相关的系统

• 批准号: 9101864
• 负责人: Juan Manfredi
• 金额: $ 6.17万
• 依托单位: University of Pittsburgh
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-06-01 至 1994-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9101864&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Partial; Differental; Equations

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.

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。