| Abstract: | 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∞ functionals. In the second part, we present some interesting connections between L∞ variational problems and weak KAM theory. As an application, we will advance the main result in Fathi and Siconolfi 17], i.e, the existence of a C1 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]. © 2007 Wiley Periodicals, Inc. |
