Kaizhi Wang

A New Kind of Lax-Oleinik Type Operator with Parameters for Time-Periodic Positive Definite Lagrangian Systems

In this paper we introduce a new kind of Lax-Oleinik type operator with parameters associated with positive definite Lagrangian systems for both the time-periodic case and the time-independent case. On one hand, the family of new Lax-Oleinik type operators with an arbitrary

The rate of convergence of new Lax–Oleinik type operators for time-periodic positive definite Lagrangian systems

{u in C(M, mathbb{R}^1)}

Aubry-Mather theory for contact Hamiltonian systems

as initial condition converges to a backward weak KAM solution in the time-periodic case, while it was shown by Fathi and Mather that there is no such convergence of the Lax-Oleinik semigroup. On the other hand, the family of new Lax-Oleinik type operators with an arbitrary

Variational principle for contact Hamiltonian systems and its applications

{u in C(M, mathbb{R}^1)}

Global generalized characteristics for the Dirichlet problem for Hamilton-Jacobi equations at a supercritical energy level.

as initial condition converges to a backward weak KAM solution faster than the Lax-Oleinik semigroup in the time-independent case.

Aubry-Mather and weak KAM theories for contact Hamiltonian systems

We establish an implicit variational principle for the contact Hamiltonian systems generated by the Hamiltonian H(x, u, p) with respect to the contact 1-form under Tonelli and Lipschitz continuity conditions.