Geodesic
Solutions of the differential inequality with a~null Lagrangian: higher integrability and removability of singularities.~I
Vladikavkazskij matematičeskij žurnal, Tome 16 (2014) no. 3, pp. 22-37

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The aim of this paper is to derive the self-improving property of integrability for derivatives of solutions of the differential inequality with a null Lagrangian. More precisely, we prove that the solution of the Sobolev class with some Sobolev exponent slightly smaller than the natural one determined by the structural assumption on the involved null Lagrangian actually belongs to the Sobolev class with some Sobolev exponent slightly larger than this natural exponent. We also apply this property to improve Hölder regularity and stability theorems of [19]. 
@article{VMJ_2014_16_3_a2,
     author = {A. A. Egorov},
     title = {Solutions of the differential inequality with a~null {Lagrangian:} higher integrability and removability of {singularities.~I}},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {22--37},
     publisher = {mathdoc},
     volume = {16},
     number = {3},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2014_16_3_a2/}
}
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A. A. Egorov. Solutions of the differential inequality with a~null Lagrangian: higher integrability and removability of singularities.~I. Vladikavkazskij matematičeskij žurnal, Tome 16 (2014) no. 3, pp. 22-37. http://geodesic.mathdoc.fr/item/VMJ_2014_16_3_a2/