Mathematical Sciences: Maximum Principles and Best Contants for Some Problems in Elliptic PDE

数学科学：椭圆偏微分方程若干问题的最大原理和最佳常数

• 批准号: 9105407
• 负责人: Gregory Verchota
• 金额: $ 6.4万
• 依托单位: Syracuse University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-06-01 至 1994-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9105407&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Maximum; Principles; Best

Optimal estimates for three general problems from the theory of elliptic differential equations will be studied. The first part of the project involves establishing an Agmon-Miranda maximum principle or showing the failure of such a principle for all constant coefficient linear elliptic equations in the dilation invariant setting of Lipschitz domain in Rn. Included here is the completion of the Lp theory in the manner of Agmon- Douglis-Nirenberg for Lipschitz domains. The second part involves strong maximum principles and best constant estimates for conditioned Brownian motion. The third part is concerned with optimal domain decomposition in the Schwarz iteration method employed in certain numerical problems.

从椭圆型微分方程理论出发，研究了三个一般问题的最优估计。项目的第一部分涉及建立Agmon-Miranda极大值原理或证明该原理在Rn中Lipschitz域的膨胀不变设置下对所有常系数线性椭圆方程失效。本文以Agmon- Douglis-Nirenberg的方式完成了Lipschitz域的Lp理论。第二部分涉及条件布朗运动的强极大值原理和最佳常数估计。第三部分讨论了Schwarz迭代法在某些数值问题中的最优区域分解问题。