Mathematical Sciences: "Unique Continuation, Quantitative Properties of Solutions and Symmetry for PDE's

数学科学：“偏微分方程的独特连续性、解的定量性质和对称性

• 批准号: 9104023
• 负责人: Nicola Garofalo
• 金额: $ 7.64万
• 依托单位: Purdue Research Foundation
• 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: 1991-07-01 至 1995-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9104023&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Unique; Continuation; Quantitative

This project will study unique continuation for subelliptic operators, Wiener's criterion and Harnack inequalities, and symmetry of boundary value problems. Unique continuation for subelliptic operators will be studied through a blend of geometric and variational techniques that allow more cases than the usual Carleman method. In the studies of symmetries the PI will continue his attempts in the solution to Schiffer's conjecture and Pompeiu's problem. The questions to be considered in this project are motivated by basic problems in geometry and mathematical physics. Their answers will contribute to a firmer understanding of fundamental scientific issues.

这个项目将研究次椭圆算子的唯一延拓，Wiener判据和Harnack不等式，以及边值问题的对称性。亚椭圆算子的唯一延拓将通过几何和变分技术的混合来研究，这些技术允许比通常的Carleman方法更多的情况。在对称性的研究中，PI将继续尝试解决希弗猜想和庞贝问题。这个项目中要考虑的问题是由几何和数学物理中的基本问题引起的。他们的答案将有助于更坚定地理解基本的科学问题。