Lasry-Lions, Lax-Oleinik and generalized characteristics  

作　　者：CHEN Cui CHENG Wei 

机构地区：[1]Department of Mathematics, Nanjing University

出　　处：《Science China Mathematics》2016年第9期1737-1752,共16页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos. 11271182 and 11471238);the National Basic Research Program of China (Grant No. 2013CB834100)

摘　　要：In the recent works, an intrinsic approach of the propagation of singularities along the generalized characteristics was obtained, even in global case, by a procedure of sup-convolution with the kernel the fundamental solutions of the associated Hamilton-Jacobi equations. In the present paper, we exploit the relations among Lasry-Lions regularization, Lax-Oleinik operators(or inf/sup-convolution) and generalized characteristics, which are discussed in the context of the variational setting of Tonelli Hamiltonian dynamics, such as Mather theory and weak KAM(Kolmogorov-Arnold-Moser) theory.In the recent works, an intrinsic approach of the propagation of singularities along the generalized characteristics was obtained, even in global case, by a procedure of sup-convolution with the kernel the fundamental solutions of the associated Hamilton-Jacobi equations. In the present paper, we exploit the relations among Lasry-Lions regularization, Lax-Oleinik operators（or inf/sup-convolution） and generalized characteristics, which are discussed in the context of the variational setting of Tonelli Hamiltonian dynamics, such as Mather theory and weak KAM（Kolmogorov-Arnold-Moser） theory.

关 键 词：Hamilton-Jacobi equations weak KAM theory generalized characteristics 

分 类 号：O175[理学—数学]