Weak KAM theorem on non compact manifolds
نویسنده
چکیده
In this paper, we consider a time independent C Hamiltonian, satisfying the usual hypothesis of the classical Calculus of Variations, on a non-compact connected manifold. Using the Lax-Oleinik semigroup, we give a proof of the existence of weak KAM solutions, or viscosity solutions, for the associated Hamilton-Jacobi Equation. This proof works also in presence of symmetries. We also study the role of the amenability of the group of symmetries to understand when the several critical values that can be associated with the Hamiltonian coincide. 2000 Mathematics Subject Classification: 49L25, 70H20, 58D19.
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