Holomorphic Singular Integrals on Non-Smooth Domains in Complex Analysis

复分析中非光滑域上的全纯奇异积分

• 批准号: 1001304
• 负责人: Loredana Lanzani
• 金额: $ 12.5万
• 依托单位: University of Arkansas
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-06-01 至 2014-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1001304&HistoricalAwards=false
• 关键词: Holomorphic; Singular; Integrals; Non; Smooth

Loredana Lanzani and her collaborators will explore a number of fundamental questions in the area of Several Complex Variables and Partial Differential Equations, with emphasis onthe ambient domain's lack of boundary regularity. To accomplish these goals Loredana Lanzani and her collaborators will develop new techniques that hinge upon an interplay of complex analysis and harmonic analysis.Several Complex Variables, Harmonic Analysis and Partial Differential Equations are major branches of mathematics. They are of paramount importance in pure and applied sciences and have vastly contributed to our present-day understanding of such basic phenomena as heat transfer and celestial mechanics.

Loredana Lanzani和她的合作者将探索多复变量和偏微分方程领域的一些基本问题，重点是环境域缺乏边界规则性。为了实现这些目标，Loredana Lanzani和她的合作者将开发新的技术，这些技术取决于复分析和调和分析的相互作用。多复变量，调和分析和偏微分方程是数学的主要分支。它们在纯科学和应用科学中具有极其重要的意义，并对我们今天对传热和天体力学等基本现象的理解做出了巨大贡献。