L∞ variational problems and weak KAM theory

In the first part of this paper, we extend several results in Crandall, Evans, and Gariepy [ 11] and Crandall and Evans [ 10] to absolute minimizers of more general L-infinity functionals. In the second part, we present some interesting connections between L-infinity variational problems and weak KAM theory. As an application, we will advance the main result in Fathi and Siconolfi [ 17], Le, the existence of a C 1 subsolution of the Hamilton-Jacobi equation. Moreover, we will propose a possible approximation of the projected Aubrey set by a variational approach that was first used by Evans in [14]. (c) 2006 Wiley Periodicals, Inc.