Mathematical Sciences: Bergman Space Inequalities

数学科学：伯格曼空间不等式

• 批准号: 9501107
• 负责人: James Michael Wilson
• 金额: $ 4.32万
• 依托单位: University of Vermont & State Agricultural College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9501107&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Bergman; Space; Inequalities

Wilson DMS-9501107 Wilson will prove weighted norm inequalities that show how the interior smoothness of solutions of certain classes of partial differential equations are controlled by the size of their boundary data. This allows one to gauge the speed of convergence of numerical approximations to the exact solutions of the pde, and to determine how perturbations of boundary data effects the rate of convergence. Partial differential equations form a basis for mathematical modeling of the physical world. The role of mathematical analysis is not so much to create the equations as it is to provide qualitative and quantitative information about the solutions. This may include answers to questions about uniqueness, smoothness and growth. In addition, analysis often develops methods for approximation of solutions and estimates on the accuracy of these approximations.

Wilson DMS-9501107 威尔逊将证明加权范数不等式，显示如何内部光滑的解决方案的某些类别的偏微分方程是由其边界数据的大小控制。 这使得人们可以测量数值逼近到偏微分方程精确解的收敛速度，并确定边界数据的扰动如何影响收敛速度。 偏微分方程是物理世界数学建模的基础。 数学分析的作用与其说是建立方程，不如说是提供关于解的定性和定量信息。 这可能包括关于独特性，平滑性和增长的问题的答案。 此外，分析经常发展出解的近似方法和对这些近似的准确性的估计。