Geometric Results for a Class of Hyperbolic Operators with Double Characteristics ,II.
Geometric Results for a Class of Hyperbolic Operators with Double Characteristics ,II.
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一类双特征双曲算子的几何结果，II．
DOI：
10.1006/jfan.1993.1104
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发表时间：
1993
影响因子：
1.7
通讯作者：
C. Parenti
中科院分区：
文献类型：
--
作者：
E. Bernardi;A. Bove;C. Parenti
设p是m阶双曲（伪）微分算子的主符号，其特征根至多为二重。设在p的双特征流形F的每一点ρ上，p的哈密顿矩阵F p，F p，f是4维Jordan块。本文证明了p的双特征曲线有极限点属于p的一个充要条件。证明了如果p的双特征曲线都不具有属于n的极限点，则p的Cauchy问题是适定的，只要低阶项满足通常的Levi条件.
Abstract Let p be the principal symbol of a hyperbolic (pseudo) differential operator of order m admitting at most double characteristic roots. Suppose that at each point ρ of the double characteristic manifold Σ of p the Hamiltonian matrix of p , F p , hasa Jordan block of dimension 4. We prove a necessary and sufficient condition on p in order that its bicharacteristic curves have limit points belonging to Σ. It is shown that if no bicharacteristic curve of p has a limit point belonging to Σ then the Cauchy problem for p is well-posed, provided the usual Levi conditions on thelower order terms are satisfied.