160 research outputs found
Long time average of first order mean field games and weak KAM theory
We show that the long time average of solutions of first order mean field
game systems in finite horizon is governed by an ergodic system of mean field
game type. The well-posedness of this later system and the uniqueness of the
ergodic constant rely on weak KAM theory
A note on the regularity of solutions of Hamilton-Jacobi equations with superlinear growth in the gradient variable
We investigate the regularity of solutions of first order Hamilton-Jacobi
equation with super linear growth in the gradient variable. We show that the
solutions are locally H\"older continuous with H\"older exponent depending only
on the growth of the Hamiltonian. The proof relies on a reverse H\"older
inequality
Regularity Results for Eikonal-Type Equations with Nonsmooth Coefficients
Solutions of the Hamilton-Jacobi equation , with
H\"older continuous and convex and positively homogeneous of
degree 1, are shown to be locally semiconcave with a power-like modulus. An
essential step of the proof is the -regularity of the
extremal trajectories associated with the multifunction generated by
H\"older regularity for viscosity solutions of fully nonlinear, local or nonlocal, Hamilton-Jacobi equations with super-quadratic growth in the gradient
Viscosity solutions of fully nonlinear, local or non local, Hamilton-Jacobi
equations with a super-quadratic growth in the gradient variable are proved to
be H\"older continuous, with a modulus depending only on the growth of the
Hamiltonian. The proof involves some representation formula for nonlocal
Hamilton-Jacobi equations in terms of controlled jump processes and a weak
reverse inequality
On a continuous time game with incomplete information
For zero-sum two-player continuous-time games with integral payoff and
incomplete information on one side, one shows that the optimal strategy of the
informed player can be computed through an auxiliary optimization problem over
some martingale measures. One also characterizes the optimal martingale
measures and compute it explicitely in several examples
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