Type: Article
Publication Date: 2022-11-10
Citations: 13
DOI: https://doi.org/10.1007/s00205-022-01828-7
Abstract We show that for constant rank partial differential operators $$\mathscr {A}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>A</mml:mi> </mml:math> whose wave cones are spanning, generalized Young measures generated by bounded sequences of $$\mathscr {A}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>A</mml:mi> </mml:math> -free measures can be characterized by duality with $$\mathscr {A}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>A</mml:mi> </mml:math> -quasiconvex integrands of linear growth. This includes a characterization of the concentration effects in such sequences that allows us to conclude that, in sharp contrast to the oscillation effects, the concentration always has $$\mathscr {A}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>A</mml:mi> </mml:math> -free structure.