Maurice Gevrey

Maurice Gevrey (1877-1944) was a French mathematician best known for his contributions to the theory of partial differential equations, particularly in the study of analytic functions and Gevrey classes.

Gevrey's research focused on the regularity properties of solutions to partial differential equations. He introduced the concept of Gevrey classes, which are function spaces that generalize the notion of analytic functions. While analytic functions have convergent Taylor series, Gevrey functions have Taylor series that may diverge, but whose coefficients satisfy certain growth conditions. These growth conditions are characterized by a parameter, often denoted by 's', that determines the degree of the Gevrey class. The smaller the 's' value, the closer the Gevrey class is to the class of analytic functions.

Gevrey classes are useful in studying the regularity of solutions to partial differential equations because they provide a framework for analyzing functions that are smoother than infinitely differentiable functions (C^∞), but not necessarily analytic. Solutions to certain types of partial differential equations, such as some parabolic equations, may belong to Gevrey classes even if they are not analytic.

Gevrey's work has had a significant impact on the development of the theory of partial differential equations and has been applied in various areas of mathematics and physics, including the study of heat equations, wave equations, and fluid dynamics. His contributions continue to be relevant in contemporary research.