We establish a framework that allows to prove Gamma-converge of functionals of Lagrangian form on spaces of trajectories based on convergence of viscosity solutions of associated Hamilton-Jacobi equations. Gamma convergence follows from a: equi-coercivity, b: Gamma convergence of the projected functional at time 0, c: convergence of the Hamiltonians that appear as Legendre transform of the Lagrangian in the path-space functional.
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