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.