The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence… Expand

SummaryWe obtain some new existence, uniqueness and stability results for ordinary differential equations with coefficients in Sobolev spaces. These results are deduced from corresponding results on… Expand

A new version of the Perona and Malik theory for edge detection and image restoration is proposed. This new version keeps all the improvements of the original model and avoids its drawbacks: it is… Expand

Abstract.We survey here some recent studies concerning what we call mean-field models by analogy with Statistical Mechanics and Physics. More precisely, we present three examples of our mean-field… Expand

This work studies two splitting algorithms for (stationary and evolution) problems involving the sum of two monotone operators with real-time requirements.Expand

We present a general method which enables us to prove the orbital stability of some standing waves in nonlinear Schrödinger equations. For example, we treat the cases of nonlinear Schrödinger… Expand