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On removable singular sets for solutions of higher order differential inequalities

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Abstract

We obtain conditions guaranteeing that weak solutions of higher order differential inequalities have a removable singularity on a compact set. These conditions depend on the fractal dimension of the singular set. For solutions of the nonlinear Poisson equation in the case of an isolated singularity, i.e. in the case where the fractal dimension of the singular set is equal to zero, they coincide with the well-known Brezis-Véron condition.

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Acknowledgements

This research is supported by RUDN University, Strategic Academic Leadership Program. The research of the first author is also supported by RSF, grant 20-11-20272.

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow Lomonosov State University, Vorobyovy Gory, Moscow, 119234, Russia

    A. A. Kon’kov

  2. Center of Nonlinear Problems of Mathematical Physics, RUDN University, Miklukho-Maklaya str. 6, Moscow, 117198, Russia

    A. A. Kon’kov & A. E. Shishkov

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  1. A. A. Kon’kov
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  2. A. E. Shishkov
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Correspondence to A. A. Kon’kov.

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Kon’kov, A.A., Shishkov, A.E. On removable singular sets for solutions of higher order differential inequalities. Fract Calc Appl Anal 26, 91–110 (2023). https://doi.org/10.1007/s13540-022-00123-2

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  • DOI: https://doi.org/10.1007/s13540-022-00123-2

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