On the Unique Solvability of a Volevic System of Linear Equations with General Singularity

Abstract

We consider a Volevic system of linear partial differential equations with general singularity, for which we establish existence and uniqueness theorems that are analogues of the Cauchy–Kowalevsky and Holmgren Theorems. Our results are generalizations of those of J. Elschner [Beiträge Anal. 12 (1978) 185–198], J. E. C. Lope [J. Math. Sci. Univ. Tokyo 6 (1999) 527–538] and H. Tahara [J. Math. Soc. Japan 34 (1982) 279–288], which are in turn generalizations of the results of M. S. Baouendi and C. Goulaouic [Comm. Pure Appl. Math. 26 (1973) 455–475].