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math.AP2012★ 28 cited
Aubry sets for weakly coupled systems of Hamilton--Jacobi equations
Andrea Davini, Maxime Zavidovique
We introduce a notion of Aubry set for weakly coupled systems of Hamilton--Jacobi equations on the torus and characterize it as the region where the obstruction to the existence of…
math.AP2012
Existence and regularity of strict critical subsolutions in the stationary ergodic setting
Andrea Davini, Antonio Siconolfi
We prove that any continuous and convex stationary ergodic Hamiltonian admits critical subsolutions, which are strict outside the random Aubry set. They make up, in addition, a den…