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.

我们建议研究对物理学家和工程师重要的各种偏微分方程的解决方案的规律性。例如，Monge-Ampere方程在时空物理学中的曲率和弦理论中的曲率模型，而Navier-Stokes方程在天气现象，飞机和容器中的流体运动模型。从理论的角度来看，重要的是要知道，我们使用的模型满足了观察到的实际现象所观察到的规则性属性。这种调查涉及对它们所满足的奇异积分和不平等的理解。