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We consider the so-called G-equation, a level set Hamilton-Jacobi equation, used as a sharp interface model for flame propagation, perturbed by an oscillatory advection in a spatio-temporal periodic environment. Assuming that the advection has suitably small spatial divergence, we prove that, as the size of the oscillations diminishes, the solutions… (More)

- Pierre Cardaliaguet, Guillaume Euvrard
- Neural Networks
- 1992

We investigate a two-player zero-sum stochastic differential game in which the players have an asymmetric information on the random payoff. We prove that the game has a value and characterize this value in terms of dual solutions of some second order Hamilton-Jacobi equation. Key-words : stochastic differential game, asymmetric information, viscosity… (More)

- Pierre Cardaliaguet
- SIAM J. Control and Optimization
- 2007

- Pierre Cardaliaguet, B. Dacorogna W. Gangbo, Nainan K Georgy
- 2000

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)

- Rainer Buckdahn, Pierre Cardaliaguet, Marc Quincampoix
- Dynamic Games and Applications
- 2011

A Hamilton-Jacobi equation involving a double obstacle problem is investigated. The link between this equation and the notion of dual solutions—introduced in [1, 2, 3] in the framework of differential games with lack of information—is established. As an application we characterize the convex hull of a function in the simplex as the unique solution of some… (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)

- Pierre Cardaliaguet, Luis Silvestre, Pierre Cardaliaguetand
- 2017

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)