370 citations · 951 across the 49 of their papers we have counts for
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Ergodic type problems and large time behaviour of unbounded solutions of Hamilton-Jacobi Equations
Guy Barles, Jean-Michel Roquejoffre
We study the large time behavior of Lipschitz continuous, possibly unbounded, viscosity solutions of Hamilton-Jacobi Equations in the whole space . The associated ergodic pro…
Some Homogenization Results for Non-Coercive Hamilton-Jacobi Equations
Guy Barles
Recently, C. Imbert & R. Monneau study the homogenization of coercive Hamilton-Jacobi Equations with a -dependence : this unusual dependence leads to a non-standard cell probl…
Nonlocal First-Order Hamilton-Jacobi Equations Modelling Dislocations Dynamics
Guy Barles, Olivier Ley
We study nonlocal first-order equations arising in the theory of dislocations. We prove the existence and uniqueness of the solutions of these equations in the case of positive and…
Error bounds for monotone approximation schemes for parabolic Hamilton-Jacobi-Bellman equations
Guy Barles, Espen R. Jakobsen
We obtain non-symmetric upper and lower bounds on the rate of convergence of general monotone approximation/numerical schemes for parabolic Hamilton Jacobi Bellman Equations by int…
Uniqueness for unbounded solutions to stationary viscous Hamilton--Jacobi equations
Guy Barles, Alessio Porretta
We consider a class of stationary viscous Hamilton--Jacobi equations as $$ \left\{\begin{array}{l} \la u-{\rm div}(A(x) \nabla u)=H(x,\nabla u)\mbox{in }Ω, u=0{on}\partialΩ\end{arr…
A New Stability Result for Viscosity Solutions of Nonlinear Parabolic Equations with Weak Convergence in Time
Guy Barles
We present a new stability result for viscosity solutions of fully nonlinear parabolic equations which allows to pass to the limit when one has only weak convergence in time of the…