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

A. A. Egorov

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arXiv · 1005.3459

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

A. A. Egorov

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Abstract

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 Hölder regularity results of \cite{Egor2008} and to establish a theorem on removability of singularities for solutions of this inequality.

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A. A. Egorov. 2010-05-19. Solutions of the Differential Inequality with a~Null Lagrangian: Regularity and Removability of Singularities. https://arxiv.org/abs/1005.3459

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