关于全特征算子的若干问题

关于全特征算子的若干问题 SOME PROBLEMS RELATED TO THE TOTALLY CHARACTERISTIC OPERATORS 陈化 1 first-author 武汉大学数学系 武汉大学数学系 本文利用偏微分方程的Gevrey类理论,讨论了具重特征的双曲型全特征算子的Cauchy问题的适定性.同时利用微局部能量估计方法研究了全特征算子的切向亚椭圆性问题.本文结果表明除了全特征椭圆型算子具切向亚椭圆性外,非椭圆的全特征算子在一般的条件下也具切向亚椭圆性. In this paper, we study the well-posedness of totally characteristic hyperbolic Cauchy problems in Gevrey classes, and by using the so-called microlocal energy method, we deal with the microlocally tangential hypoellipticity for totally characteristic operators. Our results imply that, besides the totally characteristic elliptic operators, the totally characteristic non-elliptic operators, under a certain condi- tion, are tangential hypoelliptic, as well. 全特征算子 Gevrey类 切向亚椭圆性 微局部能量估计 指标算子 全特征算子的边界谱 Totally characteristic operator Gevrey class tangential hypoellipticity microlocal energy estimate indicial operator boundary spectrum of tatally characteristic operator O175.2;O175.27 中国自然科学基金资助课题 1993-01-01 2021-04-01 1