Extensions of MoserBangert Theory: Locally Minimal Solutions [Hardcover]

This self-contained monograph presents extensions of the MoserBangert approach that include solutions of a family of nonlinear elliptic PDEs on?Rⁿ and an AllenCahn PDE model of phase transitions. After recalling the relevant MoserBangert results, Extensions of MoserBangert Theory pursues the rich structure of the set of solutions of a simpler model case, expanding upon the studies of Moser and Bangert to include solutions that merely have local minimality properties.

The work is intended for mathematicians who specialize in partial differential equations and may also be used as a text for a graduate topics course in PDEs.

This monograph presents extensions of the Moser-Bangert approach that include solutions of a family of nonlinear elliptic PDEs on?Rⁿ?and an Allen-Cahn PDE model of phase transitions. The text may be used as a text for a graduate course in PDEs.

With the goal of establishing a version for partial differential equations (PDEs) of the AubryMather 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 MoserBangert approach that include solutions of a family of nonlinear elliptic PDEs on?Rⁿ and an AllenCahn PDE model of phase transitions.

After recalling the relevant MoserBangert results, Extensions of MoserBangert Theory pursues the rich structure of the set of solutions of a simpler model case, expanding upon the studies of Moser and Bangert to include solutions that merely have local minimality properties. Subsequent chapters build upon the introductory results, making the monograph self contained.

Part I introduces a variational approacl“'