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Regularity estimates for nonlocal equations with an asymptotic property

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Abstract

In this paper we obtain \({\mathcal {C}}^{1,(\sigma -1)^-}\) regularity estimates for a class of nonlocal \({\mathcal {L}}_0(\sigma )-\)uniformly elliptic equations with an asymptotic property. We use the compactness technique to recover such regularity from the nonlocal version of the recession operator.

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Acknowledgements

The authors warmly thank the referee for a careful reading and useful comments, which improved the manuscript at several points. The first author was partially supported by FAPITEC/CAPES and CNPq. The second author was partially supported by CAPES.

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Authors and Affiliations

  1. Federal University of Sergipe (UFS), São Cristóvão, Brazil

    Disson dos Prazeres

  2. Federal University of Paraíba (UFPB), João Pessoa, Brazil

    Aelson Sobral

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  1. Disson dos Prazeres
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  2. Aelson Sobral
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Correspondence to Disson dos Prazeres.

Additional information

This article is part of the section “Theory of PDEs” edited by Eduardo Teixeira.

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dos Prazeres, D., Sobral, A. Regularity estimates for nonlocal equations with an asymptotic property. Partial Differ. Equ. Appl. 2, 33 (2021). https://doi.org/10.1007/s42985-021-00090-y

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  • DOI: https://doi.org/10.1007/s42985-021-00090-y

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