A sufficient and necessary condition for $${\mathcal {A}}$$-quasiaffinity

Abstract

We consider a homogeneous differential operator $${\mathcal {A}}$$ A and show an improved version of Murat’s condition for $${\mathcal {A}}$$ A -quasiaffine functions, provided that the operator $${\mathcal {A}}$$ A satisfies the constant rank condition. As a consequence, we obtain that affinity along the characteristic cone of $${\mathcal {A}}$$ A implies $${\mathcal {A}}$$ A -quasiaffinity if $${\mathcal {A}}$$ A admits a first order potential.