PRIVAT , Yannick

In this paper we introduce the randomised stability constant for abstract inverse problems, as a generalisation of the randomised observability constant, which was studied in the context of observability inequalities for the linear wave equation. We study the main properties of the randomised stability constant and discuss the implications for...

This article explores recent geometric optimal control techniques for the analysis of geodesics in Zermelo navigation problems on 2-spheres of revolution, focusing on accessibility and optimality properties. These techniques involve the classification of pairs \((F_0, g)\), where \(F_0\) represents the current and \(g\) is the Riemannian metric...

We consider two inverse problems related to the tokamak \textsl{Tore Supra} through the study of the magnetostatic equation for the poloidal flux. The first one deals with the Cauchy issue of recovering in a two dimensional annular domain boundary magnetic values on the inner boundary, namely the limiter, from available overdetermined data on...

In this article motivated by physical applications, the Zermelo navigation problem on the two-dimensional sphere with a revolution metric is analyzed within the framework of minimal time optimal control. The Pontryagin maximum principle is used to compute extremal curves and a neat geometric frame is introduced using the...

The functional determinant of elliptic differential operators on the circle was introduced in [3]. In the present paper, optimisation of this determinant over essentially bounded functions is studied. In the one dimensional case, existence and uniqueness of maximisers and minimisers is proved.

The functional determinant of elliptic differential operators on the circle was introduced in [3]. In the present paper, optimisation of this determinant over essentially bounded functions is studied. In the one dimensional case, existence and uniqueness of maximisers and minimisers is proved.