Mathematical Sciences: Application of the Mulilayer Free Boundary Method to Nonlinear Elliptic Equations in Convex Domains

数学科学：多层自由边界法在凸域非线性椭圆方程中的应用

• 批准号: 9102886
• 负责人: Edward Stredulinsky
• 金额: $ 3.77万
• 依托单位: University of Wisconsin-Madison
• 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: 1991-06-15 至 1994-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9102886&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Application; Mulilayer; Free

This project is concerned with the regularity theory for a class of nonlinear elliptic equations and associated variational problems involving derivatives of the rearrangement of solutions, as well as related questions concerning convex symmetrization. The main emphasis is to be placed on variational problems which are approximable by sequences of multilayer free boundary problems. Regularity and structure of the level surfaces of solutions will be studied. This project has been motivated by a model of quasi static equilibrium of confined toroidal plasmas in thermonuclear fusion research, and the study of rotational fluid flow. The technical questions to be addressed have fundamental implications in areas such as fusion energy.

该项目涉及一类非线性椭圆方程的规律性理论以及涉及解决方案重新排列的导数以及有关凸对称性的相关问题的相关变分问题。 主要的重点是将各种问题序列近似于多层边界问题的序列而言。 将研究溶液水平表面的规律性和结构。 该项目的动机是由热核融合研究中的粘液环状等离子体的准静态平衡模型以及旋转流体流量的研究。 要解决的技术问题在融合能源等领域具有根本影响。