Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 74, pp. 1-14.

Title: A Holmgren type theorem for partial differential equations
       whose coefficients are Gevrey functions
       
Author: Masaki Kawagishi (Nihon Univ., Tokyo, Japan)
 
Abstract:
 In this article, we consider a uniqueness theorem of Holmgren type
 for p-th order Kovalevskaja linear partial differential equations
 whose coefficients are Gevrey functions. We prove that the
 only $C^p$-solution to the zero initial-valued problem is
 the identically zero function. To prove this result we use the
 uniqueness theorem for higher-order ordinary differential
 equations in Banach scales.

Submitted March 28, 2010. Published May 21, 2010.
Math Subject Classifications: 35A05, 35A10, 35G10.
Key Words: Banach scale; Gevery function; Holmgren type;
           Uniqueness theorem.