Let \(\mathcal {B}\) be a homogeneous differential operator of order \(l=1\) or \(l=2\). We show that a sequence of functions of the form \((\mathcal {B}u_j)_j\) converging in the \(L^1\)-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.

让\(\mathcal {B}\)是\(l=1\)或\(l=2\)阶齐次微分算子。我们证明了\((\mathcal {B}u_j)_j\)形式的函数序列在\(L^1\) -sense 中收敛到一个紧凑的凸集K可以被修改为一个序列一致收敛到这个集合，前提是l阶导数是一致有界的。我们在整个空间、一个开放域和K上证明我们的结果的版本在一个开放的有界域上均匀地连续变化。这是 S. Müller 证明的梯度序列定理的条件推广。此外，构造了线性化等熵欧拉系统的二阶势。