Characteristic Cauchy problems for some non-Fuchsian partial differential operators
It is shown that there is a class of operators for which one can uniquely solve the characteristic Cauchy problems in the category of functions which are of class \(C^ \infty\) with respect to \(t\) and real-analytic with respect to \(x\). This class is wider than the Fuchsian operators in the sense of \textit{M. S. Baouendi} and \textit{C. Goulaouic} [Commun. Pure Appl. Math. 26, 455-475 (1973; Zbl 0264.35047)]. Moreover, the author shows for this class of operators a uniqueness theorem similar to the Holmgren theorem. In order to state the conditions, one uses the Newton polygon associated to the operator. Further, the author considers generalized Newton polygons and defines some function spaces associated to generalized Newton polygons in order to get the regularity with respect to \(t\) in the proof.
scientific article; zbMATH DE number 469076