The Mather measure and a Large Deviation Principle for the Entropy Penalized Method
نویسندگان
چکیده
We present the rate function and a large deviation principle for the entropy penalized Mather problem when the Lagrangian is generic (it is known that in this case the Mather measure μ is unique and the support of μ is the Aubry set). We assume the Lagrangian L(x, v), with x in the torus TN and v ∈ Rn, satisfies certain natural hypothesis, such as superlinearity and convexity in v, as well as some technical estimates. Consider, for each value of ǫ and h, the entropy penalized Mather problem
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