Mathematical Sciences: Microlocal Methods In Analysis

这个项目将发展偏微分方程组和几个复变量的微局部方法。主要研究一阶偏微分方程解的正则性，具有双重特征的算子的解析正则性，以及Szego核。要分析的问题建立在PI及其合作者最近的结果基础上。该项目考虑了最先进的数学问题。大量的应用数学领域将从这项研究的结果中受益。

This project will develop microlocal methods in partial differential equations and several complex variables. The main problems to be undertaken are the regularity of solutions to first order PDEs, the analytic regularity for operators with double characteristics, and the Szego kernel. The questions to be analyzed build on recent results by the PI and his collaborators. The project considers state of the art mathematical questions. Ample areas of applied mathematics will benefit from the results of this research.