The rate of convergence of the Lax-Oleinik semigroup-degenerate fixed point case |
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| Authors: | WANG KaiZhi & YAN Jun School of Mathematical Sciences Key Lab of Mathematics for Nonlinear Science Fudan University Shanghai China School of Mathematics Jilin University Changchun |
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| Affiliation: | WANG KaiZhi1,2 & YAN Jun1 1School of Mathematical Sciences and Key Lab of Mathematics for Nonlinear Science,Fudan University,Shanghai 200433,China,2School of Mathematics,Jilin University,Changchun 130012 |
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| 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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| Keywords: | Hamiltonian system weak KAM theorem Lax-Oleinik semigroup |
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