Minimizers of Dirichlet functionals on the n−torus and the Weak KAM Theory
نویسنده
چکیده
Given a probability measure μ on the n−torus T and a rotation vector k ∈ R, we ask wether there exists a minimizer to the integral ∫ Tn |∇φ + k|2dμ. This problem leads, naturally, to a class of elliptic PDE and to an optimal transportation (MongeKantorovich) class of problems on the torus. It is also related to higher dimensional Aubry-Mather theory, dealing with invariant sets of periodic Lagrangians, and is known as the ”Weak-KAM theory”.
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تاریخ انتشار 2007