Boundary Values of Hyperfunction Solutions of Linear Partial Differential Equations (佐藤の超函数とその応用)
Boundary Values of Hyperfunction Solutions of Linear Partial Differential Equations (佐藤の超函数とその応用)
复制标题
线性偏微分方程超函数解的边界值（佐藤超函数及其应用）
DOI：
10.2977/prims/1195193784
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发表时间：
1971
影响因子：
0.7
通讯作者：
T. Kawai
中科院分区：
文献类型：
--
作者：
H. Komatsu;T. Kawai
设P（#，D）是Rn+1中区域V中具有真实的解析系数的线性偏微分算子，SC_n是关于P（#，D）的非特征的真实的解析超曲面.证明了P（x，D）u = Q在V\S的一侧的超函数解u在S上有边值，这些边值是在5上的n元超函数. H. Komatsu [_6~] and P. Schapira Q8]在P（x，J 9）是椭圆形的情况下。他们的方法稍加修改就适用于一般算子。在§1中，我们证明了初值在δ上的对偶方程的Cauchy-Kowalevsky定理等价于支撑在δ上的超函数s被微分算子P（x，D）整除的定理。我们在§ 2中定义了边值，并证明了Cauchy问题的超函数解的唯一性。
Let P(#, D} be a linear partial differential operator with real analytic coefficients in a domain V in Rn+1 and let SC^ be a real analytic hypersurface non-characteristic with respect to P(#, D). The purpose of this paper is to show that every hyperfunction solution u of P(x, D)u = Q on one side of V\S has boundary values on S which are hyperfunctions of n variables on 5. This fact has been proved by H. Komatsu [_6~] and P. Schapira Q8] in the case where P(x, J9) is elliptic. Their method applies with minor modifications to the general operators. In §1 we show that the Cauchy-Kowalevsky theorem for the dual equation with the initial values on 5 is equivalent to a theorem of division of hyperfunction s with supports in 5 by the differential operator P(x, D). We define the boundary values in § 2 and prove the uniqueness of hyperfunction solutions of the Cauchy problems.