Probleme de Neumann pour l'equation de Monge–Ampere sur les varietes Riemanniennes

AbstractLet (M,g) be a C∞ compact Riemannian manifold with strictly convex boundary. Let f∈C∞(T★M×R) and ϕ∈C∞(∂M×R). Under various hypothesis on f and ϕ, using either continuity method, iterative procedure or fixed point argument, combined with C2,α a priori estimates, we solve Monge–Ampère equations, with nonlinear Neumann boundary condition, of the following form:log(det∇iju)=f(x,du;u)inM,∂u∂ν=ϕ(x,u)on∂M