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A note on the continuity of minors in grand Lebesgue spaces

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Abstract

We present a simple proof of the continuity, in the sense distributions, of the minors of the differential matrices of mappings belonging to grand Sobolev spaces. Such function spaces were introduced in connection with a problem on minimal integrability of the Jacobian and are useful in certain aspects of geometric function theory and partial differential equations.

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Acknowledgements

I would like to thank Professor Sergey Vodopyanov and my great friend Dr. Ian McGregor for the numerous discussions on and useful comments about this paper.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, 4 Acad. Koptyug avenue, Novosibirsk, Russia, 630090

    Anastasia Molchanova

  2. Peoples’ Friendship University, 6 Miklukho-Maklaya str., Moscow, Russia, 117198

    Anastasia Molchanova

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  1. Anastasia Molchanova
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Correspondence to Anastasia Molchanova.

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This work was supported by a Grant of the Russian Foundation of the Russian Science Foundation (Agreement No. 16-41-02004).

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Molchanova, A. A note on the continuity of minors in grand Lebesgue spaces. J. Fixed Point Theory Appl. 21, 49 (2019). https://doi.org/10.1007/s11784-019-0686-y

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  • DOI: https://doi.org/10.1007/s11784-019-0686-y

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