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E-mail: rio@smath.ru
DOI: 10.23671/VNC.2014.3.10232
Solutions of the differential inequality with a null Lagrangian: higher integrability and removability of singularities. I
Egorov A. A.
Vladikavkaz Mathematical Journal 2014. Vol. 16. Issue 3.
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 Holder regularity and stability theorems of [19].
Keywords: null Lagrangian, higher integrability, self-improving regularity, Holder regularity, stability of classes of mappings
For citation: Egorov A. A. Solutions of the differential inequality with a null Lagrangian: higher integrability and removability of singularities. I // Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], vol. 16, no. 3, pp. 22-37. DOI 10.23671/VNC.2014.3.10232
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