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 Vladikavkaz. Mat. Zh., 2014, Volume 16, Number 3, Pages 22–37 (Mi vmj510)

Solutions of the differential inequality with a null Lagrangian: higher integrability and removability of singularities. I

A. A. Egorovab

a Sobolev Institute of Mathematics, RUSSIA, 630090, Novosibirsk, Koptyug Avenue, 4
b Novosibirsk State University, RUSSIA, 630090, Novosibirsk, Pirogova Str., 2

Abstract: 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].

Key words: null Lagrangian, higher integrability, self-improving regularity, Hölder regularity, stability of classes of mappings.

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UDC: 517.957+517.548
MSC: Primary 30C65; Secondary 35F20, 35A15, 35B35, 26B25
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Citation: A. A. Egorov, “Solutions of the differential inequality with a null Lagrangian: higher integrability and removability of singularities. I”, Vladikavkaz. Mat. Zh., 16:3 (2014), 22–37

Citation in format AMSBIB
\Bibitem{Ego14} \by A.~A.~Egorov \paper Solutions of the differential inequality with a~null Lagrangian: higher integrability and removability of singularities.~I \jour Vladikavkaz. Mat. Zh. \yr 2014 \vol 16 \issue 3 \pages 22--37 \mathnet{http://mi.mathnet.ru/vmj510} 

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This publication is cited in the following articles:
1. A. A. Egorov, “Solutions of the differential inequality with a null Lagrangian: higher integrability and removability of singularities. II”, Vladikavk. matem. zhurn., 16:4 (2014), 41–48
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