Elliptic Boundary Value Problems in Non-Smooth Domains

非光滑域中的椭圆边值问题

• 批准号: 0500257
• 负责人: Zhongwei Shen
• 金额: $ 7.2万
• 依托单位: University of Kentucky Research Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-07-01 至 2008-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0500257&HistoricalAwards=false
• 关键词: Elliptic; Boundary; Value; Problems; Non

Elliptic Boundary value problems in non-smooth domains.Abstract of proposed researchZhongwei ShenThis research project centers on problems in the area of partial differential equations in domains with non-smooth boundaries. The PI will study the solvability of boundary value problems on the class of bounded Lipschitz domains. This is a dilation-invariant class of domains which have boundaries that are the graphs of Lipschitz functions. The main focus will be on boundary value problems for second order elliptic systems and higher-order elliptic equations with Lp boundary data. He will also investigate boundary value problems in convex domains.This research lies at the interface of harmonic analysis and partial differential equations.The goal of the project is to establish useful regularity estimates for solutions under physically realistic assumptions on the domain as well as on the boundary data. In many applied problems of elasticity, aero- and hydrodynamics and electro-magnetic wave scattering, the boundary value problems for the governing equations are posed in domains with rough boundaries. The results of this project will provide some mathematical foundations and analytical tools for these applications.

非光滑域中的椭圆边值问题。研究摘要沉忠伟本研究项目集中于非光滑边界域中的偏微分方程领域的问题。 PI 将研究有界 Lipschitz 域类上边值问题的可解性。这是一类膨胀不变的域，其边界是 Lipschitz 函数的图。主要重点是二阶椭圆系统和具有 Lp 边界数据的高阶椭圆方程的边值问题。他还将研究凸域中的边值问题。这项研究位于调和分析和偏微分方程的接口。该项目的目标是在域和域的物理现实假设下为解建立有用的规律性估计。边界数据。在弹性、空气动力学、流体动力学以及电磁波散射等许多应用问题中，控制方程的边值问题是在具有粗糙边界的域中提出的。该项目的结果将为这些应用提供一些数学基础和分析工具。