113 citations · 350 across the 9 of their papers we have counts for
9 papers
Convergence of the solutions of the nonlinear discounted Hamilton-Jacobi equation: The central role of Mather measures
Qinbo Chen, Albert Fathi, Maxime Zavidovique +1
Given a continuous Hamiltonian defined on , where is a closed connected manifold, we study viscosity solutions, $u_λ: M\…
Singularities of solutions of time dependent Hamilton-Jacobi equations. Applications to Riemannian geometry
Piermarco Cannarsa, Wei Cheng, Albert Fathi
If is a uniformly continuous viscosity solution of the evolution Hamilton-Jacobi equation where is a not necessaril…
Convergence of the solutions of the discounted equation: the discrete case
Andrea Davini, Albert Fathi, Renato Iturriaga +1
We derive a discrete version of the results of our previous work. If is a compact metric space, a continuous cost function and , the u…
Weak KAM theorem on non compact manifolds
Albert Fathi, Ezequiel Maderna
In this paper, we consider a time independent Hamiltonian, sa\-tisfying the usual hypothesis of the classical Calculus of Variations, on a non-compact connected manifold. Usi…
Convergence of the solutions of the discounted equation
Andrea Davini, Albert Fathi, Renato Iturriaga +1
We consider a continuous coercive Hamiltonian on the cotangent bundle of the compact connected manifold which is convex in the momentum. If is the visco…
Ilmanen's Lemma on Insertion of C Functions
Albert Fathi, Maxime Zavidovique
We give a proof of Ilmanen's lemma, which asserts that between a locally semi-convex and a locally semi-concave function it is possible to find a C function.