{mathcal {A}}-Variational Principles

Abstract

Though the {mathcal {A}}-quasiconvexity condition has been fully explored since its introduction, no explicit examples of associated variational principles have been considered except in the classical {text {curl}}-case. Our aim is to propose such a family of problems in the {text {div}}{-}{text {curl}}-situation, and explore the corresponding {mathcal {A}}-polyconvexity condition as the main structural assumption to ensure weak lower semicontinuity and existence results.