UNIQUENESS AND SOLVABILITY OF THE SINGULAR CAUCHY PROBLEM IN GEVREY SPACES

The present work aims to generalize the global results of [7] where the coefficients of the Fuchsian principal part are assumed to be constant.We consider a more general Fuchsian operator whose coefficients of the Fuchsian principal part are of Gevrey classes.We prove the global existence and uniqueness of a solution in the space of sufficiently differentiable functions with respect to the Fuchsian variable and in Gevrey spaces with respect to the other variables.Contrary to [7] where the study is restricted to projective Gevrey spaces, we consider both projective and classical Gevrey spaces.