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General theory of PDE and Gevrey classes. (English) Zbl 0864.35130

Qi, Min-You (ed.) et al., General theory of partial differential equations and microlocal analysis. Proceedings of a workshop, ICTP, Trieste, Italy, September 4–15, 1995. Harlow: Longman. Pitman Res. Notes Math. Ser. 349, 6-81 (1996).
This paper is divided into four sections. In the first one, the authors recall basic definitions of the general theory of partial differential equations, of Gevrey classes and ultradistributions, and of Gevrey microlocal analysis. In the second one, the Cauchy problem is studied in the framework of Gevrey classes. Several results of microlocal analysis in Gevrey classes and questions of Gevrey hypoellipticity and solvability are discussed in Section 3. Finally, Gevrey microlocal analysis for nonlinear partial differential equations is treated in the last section.
For the entire collection see [Zbl 0845.00043].

MSC:

35S05 Pseudodifferential operators as generalizations of partial differential operators
35A27 Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs
35S50 Paradifferential operators as generalizations of partial differential operators in context of PDEs
35L30 Initial value problems for higher-order hyperbolic equations
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