Subelliptic nonlinear equations and function theory

次椭圆非线性方程和函数论

• 批准号: 5149-2010
• 负责人: Sawyer, Eric
• 金额: $ 1.46万
• 依托单位: McMaster University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2013
• 资助国家: 加拿大
• 起止时间: 2013-01-01 至 2014-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=520771
• 关键词: Subelliptic; nonlinear; equations; function; theory

We propose to investigate the regularity of solutions to various partial differential equations that model phenomena important to physicists and engineers. For example, the Monge-Ampere equation models curvature in space time and string theories in theoretical physics and the Navier-Stokes equations model the motions of fluids in weather phenomena, airplanes and vessels. From a theoretical perspective, it is important to know that the model we are using satisfies the regularity properties observed of the actual phenomenon being modelled. Such investigations involve an understanding of singular integrals and the inequalities they satisfy.

我们建议研究各种偏微分方程解的规律性，这些偏微分方程对物理学家和工程师来说很重要的现象建模。例如，蒙日-安培方程对时空曲率和理论物理中的弦理论进行建模，纳维-斯托克斯方程对天气现象、飞机和船舶中的流体运动进行建模。从理论角度来看，重要的是要知道我们使用的模型满足所建模的实际现象所观察到的规律性。此类研究涉及对奇异积分及其满足的不等式的理解。