Adaptation of the generic PDE's results to the notion of prevalence

Romain Joly (1)

1 IF - Institut Fourier

Many generic results have been proved, especially concerning the qualitative behaviour of solutions of partial differential equations. Recently, a new notion of "almost always", the prevalence, has been developped for vectorial spaces. This notion is interesting since, for example, prevalence sets are equivalent to the full Lebesgue measure sets in finite dimensional spaces. The purpose of this article is to adapt the generic PDE's results to the notion of prevalence. In particular, we consider the cases where Sard-Smale theorems or arguments of analytic perturbations of the parameters are used.

Mots clés: prevalence; genericity; Smale theorem; Sard-Smale theorem

Domaines: Equations aux dérivées partielles [math.AP]

Romain Joly. Adaptation of the generic PDE's results to the notion of prevalence. Journal of Dynamics and Differential Equations, 2007, 19, pp.967-983. ⟨hal-00288321⟩