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.
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)
