3 papers
math.NA2026
A nonsmooth extension of the Brezzi-Rappaz-Raviart approximation theorem via metric regularity techniques and applications to nonlinear PDEs
Jules Berry, Olivier Ley, Francisco José Silva
We generalize the Brezzi-Rappaz-Raviart approximation theorem, which allows to obtain existence and a priori error estimates for approximations of solutions to some nonlinear parti…
math.OC2026
Gradient extremals, talwegs, valleys, and directional alignment for generic gradient descent
Pascal Bégout, Jérôme Bolte, Thomas Mariotti +1
Gradient extremals are loci along which the gradient is an eigenvector of the Hessian. These objects provide a natural geometric framework connecting several notions, notably valle…
math.AP2024
Approximation and perturbations of stable solutions to a stationary mean field game system
Jules Berry, Olivier Ley, Francisco J Silva
This work introduces a new general approach for the numerical analysis of stable equilibria to second order mean field games systems in cases where the uniqueness of solutions may…