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We prove a theorem on self-improving regularity for derivatives of solutionsof the inequality $F(v'(x))\le KG(v'(x))$ constructed by means of a quasiconvexfunction $F$ and a null Lagrangian $G$. We apply this theorem to improve thestability and H\"older regularity results of \cite{Egor2008} and to establish atheorem on removability of singularities for solutions of this inequality.

Solutions of the Differential Inequality with a~Null Lagrangian: Regularity and Removability of Singularities