The convergence of Lax-Oleinik semigroup for time-periodic Lagrangian |
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Authors: | Xia Li |
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Affiliation: | 1. School of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou, 215009, China
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Abstract: | In this article, the convergence of so-called Lax-Oleinik semigroup is studied for time-periodic Lagrangian systems when the degree of freedom is greater than 2. Under certain conditions, we show that the Lax-Oleinik semigroup converges if the rotation vector is completely irrational. Removing such conditions, we will give another kind of convergence of the sequence F c ((x, s), (x′, s′ +T n )), the convergence of which is closely related to the Lax-Oleinik semigroup. |
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Keywords: | Lax-Oleinik semigroup Lagrangian systems Hamilton-Jacobi equation |
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