The "Viscosity Solutions and Applications" Group

Participants : Guy Barles, Christine Georgelin, Olivier Ley, Ali Srour, Thierry Tabet Tchamba

What are Viscosity Solutions?

The notion of viscosity solution is a notion of weak solution for nonlinear, possibly degenerate, elliptic and parabolic equations ; it is used in particular for equations in non-divergence form.  This notion of solutions has shown its efficiency in a lot of domains of applications including optimal control and differential games, geometric motions and front propagation problems, finance, image theory...

Participation to research programs

The TMR Network "Viscosity Solutions and Their Applications" is over but preprints are still available on the web site

The "Working Group on Viscosity Solutions and Their Applications"

The ACI project "Motions of interfaces with nonlocal terms" . Coordinator : Elisabeth Rouy (Ecole Centrale de Lyon).

The ANR project MICA (Motions of Interfaces, Computations and Applications). Coordinator : Antonin Chambolle (CMAP, Ecole Polytechnique)

The ANR project KAMFAIBLE (Hamilton-Jacobi and weak KAM theory). Coordinator : Albert Fathi (ENS Lyon)

Current research activities

Quasilinear parabolic equations, unbounded solutions and geometric equations

Convergence of numerical schemes

Front propagations, geometrical approach and applications

Regularity of viscosity solutions for quasilinear parabolic equations

Boundary conditions in the viscosity sense

Evolution equations with a L¹ time-dependence

Uniqueness properties of viscosity solutions and applications

List of recent publications (--->)

Other publications (--->)