Mathematical Sciences: Viscosity Solutions of Nonlinear Partial Differential Equations

数学科学：非线性偏微分方程的粘度解

• 批准号: 9101799
• 负责人: Robert Jensen
• 金额: $ 5.99万
• 依托单位: Loyola University of Chicago
• 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: 1991-06-01 至 1993-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9101799&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Viscosity; Solutions; Nonlinear

This project will consider viscosity solutions for partial differential equations. Uniqueness of viscosity solutions to second order elliptic equations with measurable coefficients, minimal surface equations, the p-Laplacian, and certain Cauchy problems in bounded domains will be studied. Based on preliminary results, various maximum principles and regularity theory will be developed. While this project is aimed at theoretical aspects of partial differential equations, the results have almost immediate applications in areas such as control theory and finance.

该项目将考虑部分粘度解决方案 微分方程 粘度溶液的均一性 二阶可测系数椭圆方程 最小曲面方程，p-Laplacian，和某些Cauchy 将研究有界域中的问题。 基于 初步结果，各种极大值原理和规律 理论将得到发展。 虽然这个项目的目的是在理论方面， 偏微分方程，结果几乎立即 在控制理论和金融等领域的应用。