Osaka Journal of Mathematics

Global Fuchsian Goursat problem in the class of holomorphic-Gevrey functions

Malika Belarbi, Takeshi Mandai, and Mustapha Mechab

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Abstract

The first and the third authors have proved the global existence of holomorphic solutions to partial differential equations with several Fuchsian variables in the sense of N.S. Madi, under some assumptions on some coefficients and on the Fuchsian characteristic polynomial. This article shows a similar global existence of solutions which are holomorphic with respect to Fuchsian variables and of projective Gevrey class with respect to non-Fuchsian variables. The proof is based on the concept of formal norms of Leray-Waelbroeck and the application of Gevrey's operator of C. Wagschal.

Article information

Source
Osaka J. Math., Volume 44, Number 2 (2007), 255-283.

Dates
First available in Project Euclid: 5 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1183667981

Mathematical Reviews number (MathSciNet)
MR2351002

Zentralblatt MATH identifier
1138.35004

Subjects
Primary: 35D05
Secondary: 35A07 35A20: Analytic methods, singularities

Citation

Belarbi, Malika; Mandai, Takeshi; Mechab, Mustapha. Global Fuchsian Goursat problem in the class of holomorphic-Gevrey functions. Osaka J. Math. 44 (2007), no. 2, 255--283. https://projecteuclid.org/euclid.ojm/1183667981


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