非亚椭圆常系数线性偏微分方程和组全局解的正则性

Global Regularity of Solutions for Non-hypoelliptic Linear Partial Differential Equations and Systems with Constant Coefficients

本文运用Paley—Wiener定理、Eskin定理和作者对这两个定理的一个推广,讨论了实特征点集是空集或紧集的常系数线性偏微分方程和组全局解的正则性,推广了Schwartz定理。

By using the Paley-Wiener theorem,Eskin theorem and a generalization of thesetheorems by the author,the global regularity of linear partial differential equations andsystems with constant coefficients and compact characteristic sets is studied, and theSchwartz theorem is generalized.