Weak KAM Theorem for a Class of Infinite-Dimensional Lagrangian systems

Abstract

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 $M\in L^2(I)$.

arXiv comment14 pages

References in corpus (2)

• Weak KAM theorem on non compact manifolds
• A new kind of Lax-Oleinik type operator with parameters for time-periodic positive definite Lagrangian systems