摘要
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.
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.
基金
supported by National Natural Science Foundation of China (Grant No. 11001100)
China Postdoctoral Science Foundation (Grant No.20100470645)
Shanghai Postdoctoral Science Foundation (Grant No. 11R21412100)
the Young Fund of the College of Mathematics at Jilin University
supported by National Natural Science Foundation of China(Grant No. 10971093)
National Basic Research Program of China (973 Program) (Grant No. 2007CB814800)
