Extensions of Moser Bangert theory : locally minimal solutions With the goal of establishing a version for partial differential equations (PDEs) of the Aubry Mather theory of monotone twist maps Moser and then Bangert studied solutions of their model equations that possessed certain minimality and monotonicity properties. This monograph presents extensions of the Moser Bangert approach that include solutions of a family of nonlinear elliptic PDEs on R[superscript n] and an Allen Cahn PDE model of phase transitions. P. [4] of cover