Oscillation and concentration in sequences of PDE constrained measures

Abstract

We show that for constant rank partial differential operators $\mathcal{A}$, generalized Young measures generated by sequences of $\mathcal{A}$-free measures can be characterized by duality with $\mathcal{A}$-quasiconvex integrands of linear growth.

arXiv comment20 pages

References in corpus (6)

• On Rank-One Convex Functions that are homogeneous of Degree One
• Young Measures Generated by Ideal Incompressible Fluid Flows
• Potentials for $\mathcal{A}$-quasiconvexity
• Characterization of generalized Young measures generated by symmetric gradients
• Quasiconvexity, null Lagrangians, and Hardy space integrability under constant rank constraints
• On the necessity of the constant rank condition for $L^p$ estimates

Cited by in corpus (2)

• Remarks on Ornstein's non-inequality in ${\mathbb{R}}^{2\times 2}$
• On Scaling Properties for a Class of Two-Well Problems for Higher Order Homogeneous Linear Differential Operators