Pierre Cardaliaguet

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We study the Hamilton-Jacobi equation { F (Du) = 0 a.e. in Ω u = φ on ∂Ω (0.1) where F : IR −→ IR is not necessarily convex. When Ω is a convex set, under technical assumptions our first main result gives a necessary and sufficient condition on the geometry of Ω and on Dφ for (0.1) to admit a Lipschitz viscosity solution. When we drop the convexity(More)
The paper investigates the long time average of the solutions of Hamilton-Jacobi equations with a non coercive, non convex Hamiltonian in the torus R2/Z2. We give nonresonnance conditions under which the long-time average converges to a constant. In the resonnant case, we show that the limit still exists, although it is non constant in general. We compute(More)
We analyze a (possibly degenerate) second order mean field games system of partial differential equations. The distinguishing features of the model considered are (1) that it is not uniformly parabolic, including the first order case as a possibility, and (2) the coupling is a local operator on the density. As a result we look for weak, not smooth,(More)
We show that solutions of time-dependent degenerate parabolic equations with superquadratic growth in the gradient variable and possibly unbounded right-hand side are locally C . Unlike the existing (and more involved) proofs for equations with bounded right-hand side, our arguments rely on constructions of suband supersolutions combined with improvement of(More)