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].