Potentials for $\mathcal{A}$-quasiconvexity

Abstract

We show that each constant rank operator $\mathcal{A}$ admits an exact potential $\mathbb{B}$ in frequency space. We use this fact to show that the notion of $\mathcal{A}$-quasiconvexity can be tested against compactly supported fields. We also show that $\mathcal{A}$-free Young measures are generated by sequences $\mathbb{B}{u}_j$, modulo shifts by the barycentre.

15 pages; to appear in Calculus of Variations and Partial Differential Equations

Cited by in corpus (8)

• Quasiconvexity, null Lagrangians, and Hardy space integrability under constant rank constraints
• Oscillation and concentration in sequences of PDE constrained measures
• Compensated compactness: continuity in optimal weak topologies
• On Scaling Properties for Two-State Problems and for a Singularly Perturbed $T_3$ Structure
• On Scaling Properties for a Class of Two-Well Problems for Higher Order Homogeneous Linear Differential Operators
• A data-driven approach to viscous fluid mechanics -- the stationary case
• Syzygies, constant rank, and beyond
• A variational view on constitutive laws in parabolic problems