Weak KAM Theorem for a Class of Infinite-Dimensional Lagrangian systems
  In this paper, we study infinite-dimensional Lagrangian systems where the potential functions are periodic, rearrangement invariant and weakly upper semicontinuous. And we prove that there exists a calibrated curve for every $M\in L^{2}(I)$. 
Guanghua Shi and Cheng Yang
math.DS