Zeitschrift für Analysis und ihre Anwendungen 24 (2005), No. 2, 317--326
Copyright Heldermann Verlag 2005
On the Unique Solvability of a Volevic System of Linear Equations with General Singularity
José Ernie C. Lope
Dept. of Mathematics, University of the Philippines, Diliman, 1101 Quezon City, Philippines
ernie@math.upd.edu.ph
José Maria L. Escaner IV
Dept. of Mathematics, University of the Philippines, Diliman, 1101 Quezon City, Philippines
joma@math.upd.edu.ph
Carlene P. Arceo
Dept. of Mathematics, University of the Philippines, Diliman, 1101 Quezon City, Philippines
cayen@math.upd.edu.ph
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].
Keywords: Volevic system, singular partial differential equations.
MSC: 35A10; 35A20, 35G05
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