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: 2014
• 资助国家: 加拿大
• 起止时间: 2014-01-01 至 2015-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=544242
• 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.

我们建议调查各种偏微分方程模型的物理学家和工程师的重要现象的解决方案的规律性。例如，蒙吉-安培方程模拟时空中的曲率和理论物理学中的弦理论，而纳维尔-斯托克斯方程模拟天气现象、飞机和船只中的流体运动。从理论的角度来看，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。这样的调查涉及奇异积分和他们满足的不等式的理解。