$${\mathcal {A}}$$-Variational Principles
Luís Bandeira, Pablo Pedregal · Milan Journal of Mathematics · 2023
Abstract Though the $${\mathcal {A}}$$ A -quasiconvexity condition has been fully explored since its introduction, no explicit examples of associated variational principles have been considered except in the classical $${\text {curl}}$$ curl -case. Our aim is to propose such a family of problems in the $${\text {div}}{-}{\text {curl}}$$ div - curl -situation, and explore the corresponding $${\mathcal {A}}$$ A -polyconvexity condition as the main structural assumption to ensure weak lower semicontinuity and existence results.