The rate of convergence of the Lax-Oleinik semigroup-degenerate fixed point case  

作　　者：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, China 

出　　处：《Science China Mathematics》2011年第3期545-554,共10页中国科学：数学（英文版）

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)

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.

关 键 词：Hamiltonian system weak KAM theorem Lax-Oleinik semigroup 

分 类 号：O152.7[理学—数学]