Geodesic
A Holmgren type theorem for partial differential equations whose coefficients are Gevrey functions
Electronic journal of differential equations, Tome 2010 (2010)
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.
Classification : 35A05, 35A10, 35G10
Keywords: Banach scale, gevery function, holmgren type, uniqueness theorem 
@article{EJDE_2010__2010__a152,
     author = {Kawagishi,  Masaki},
     title = {A {Holmgren} type theorem for partial differential equations whose coefficients are {Gevrey} functions},
     journal = {Electronic journal of differential equations},
     year = {2010},
     volume = {2010},
     zbl = {1191.35012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a152/}
}
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%J Electronic journal of differential equations
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Kawagishi,  Masaki. A Holmgren type theorem for partial differential equations whose coefficients are Gevrey functions. Electronic journal of differential equations, Tome 2010 (2010). http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a152/