We establish the Mather theory for a type of piecewise smooth and positive definite Lagrangian systems.It models a mechanical system subject to external impulsive forcing.We show the existence of the minimal measure a...We establish the Mather theory for a type of piecewise smooth and positive definite Lagrangian systems.It models a mechanical system subject to external impulsive forcing.We show the existence of the minimal measure and the Lipschitz property of Aubry set.In addition,the weak KAM solution to this kind of piecewise smooth Lagrangian is also established.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11201222 and 11171146)Basic Research Program of Jiangsu Province(Grant No.BK2008013)
文摘We establish the Mather theory for a type of piecewise smooth and positive definite Lagrangian systems.It models a mechanical system subject to external impulsive forcing.We show the existence of the minimal measure and the Lipschitz property of Aubry set.In addition,the weak KAM solution to this kind of piecewise smooth Lagrangian is also established.