Mathematical Sciences: Partial Differential Equations and Several Complex Variables

本课题将研究与多个复变量相关的线性偏微分方程解的正则性和可解性。内容包括Cauchy-Riemann和切向Cauchy-Riemann问题的局部和整体可解性、解的存在性和正则性、Cauchy-Riemann算子的闭域性质和局部可嵌入性、算子的解析亚椭圆性和CR函数。这个项目的结果将有助于理解科学和工程中出现的方程的基本行为。

This project will study regularity and solvability of linear partial differential equations related to several complex variables. This will include local and global solvability, existence and regularity of solutions to the Cauchy-Riemann and tangential Cauchy-Riemann problems, the closed range property and local embeddability of Cauchy-Riemann operators, analytic hypoellipticity of operators, and CR functions. Results from this project will contribute to understanding fundamental behavior of equations arising in science and engineering.