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

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

2010-05-19

arxiv.org/abs/1005.3459v1

Mathematics

Analysis of PDEs

Scientific paper

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

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