A weaker notion of convexity for Lagrangians not depending solely on velocities and positions.

In dynamical systems, one often encounters actions A ≡ RΩLx, v(x)%dx which
depend only on v, the velocity of the system and on % the distribution of the particles. In
this case, it is well–understood that convexity of L(x, ·) is the right notion to study variational
problems. In this talk, we consider a weaker notion of convexity which seems appropriate
when the action depends on other quantities such as electro–magnetic fields. Thanks to the
introduction of a gauge, we will argue why our problem reduces to understanding the relaxation
of a functional defined on the set of differential forms (Joint work with B. Dacorogna).

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