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Let    $$\mathcal {B}$$  B be a homogeneous differential operator of order    $$l=1$$  l = 1 or    $$l=2$$  l = 2 . We show that a sequence of functions of the form    $$(\mathcal {B}u_j)_j$$  ( B u j ) j converging in the    $$L^1$$  L 1 -sense to a compact, convex set  K  can be modified into a sequence converging uniformly to this set provided that the derivatives of order  l  are uniformly bounded. We prove versions of our result on the whole space, an open domain, and for  K  varying uniformly continuously on an open, bounded domain. This is a conditional generalization of a theorem proved by S. Müller for sequences of gradients. Moreover, a potential of order two for the linearized isentropic Euler system is constructed.

Müller–Zhang truncation for general linear constraints with first or second order potential