Lagrangian Dynamics on an infinite-dimensional torus; a Weak KAM theorem
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چکیده
The space L(0, 1) has a natural Riemannian structure on the basis of which we introduce an L(0, 1)–infinite dimensional torus T. For a class of Hamiltonians defined on its cotangent bundle we establish existence of a viscosity solution for the cell problem on T or, equivalently, we prove a Weak KAM theorem. As an application, we obtain existence of absolute action-minimizing solutions of prescribed rotation number for the one-dimensional nonlinear Vlasov system with periodic potential.
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تاریخ انتشار 2009