On Continuation of Gevrey Class Solutions of Linear Partial Differential Equations

J. Math. Sci. Univ. Tokyo
Vol. 4 (1997), No. 3, Page 551--593.

Kaneko, Akira
On Continuation of Gevrey Class Solutions of Linear Partial Differential Equations
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Abstract:
We give a sufficient condition for the removability of thin singularities of Gevrey class solutions of linear partial differential equations. In \S 1 we give a sufficient condition for the removability in the case of equations with constant coefficients. Then in \S 2 we discuss the necessity of the condition and construct non-trivial solutions with irremovable thin singularities for some class of equations. In \S 3 we give a sufficient condition for the removability of thin singularities of Gevrey class solutions in the case of equations with real analytic coefficients.

Mathematics Subject Classification (1991): 35G05, 35B60, 35E20
Mathematical Reviews Number: MR1484602

Received: 1996-04-11