Abstract
For the standard Lagrangian in classical mechanics, which is defined as the kinetic energy of the system minus its potential energy, we study the rate of convergence of the corresponding Lax-Oleinik semigroup. Under the assumption that the unique global minimum point of the Lagrangian is a degenerate fixed point, we provide an upper bound estimate of the rate of convergence of the semigroup.
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Wang, K., Yan, J. The rate of convergence of the Lax-Oleinik semigroup-degenerate fixed point case. Sci. China Math. 54, 545–554 (2011). https://doi.org/10.1007/s11425-010-4138-9
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DOI: https://doi.org/10.1007/s11425-010-4138-9