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Local Hölder continuity for fractional nonlocal equations with general growth

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Abstract

We study generalized fractional p-Laplacian equations to prove local boundedness and Hölder continuity of weak solutions to such nonlocal problems by finding a suitable fractional Sobolev-Poincaré inquality.

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Acknowledgements

We would like to thank referees for many helpful comments.

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Authors and Affiliations

  1. Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul, 08826, South Korea

    Sun-Sig Byun

  2. Department of Mathematical Sciences, Seoul National University, Seoul, 08826, South Korea

    Hyojin Kim

  3. Department of Mathematics, Sogang University, Seoul, 04107, South Korea

    Jihoon Ok

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  1. Sun-Sig Byun
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  2. Hyojin Kim
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S. Byun was supported by NRF-2021R1A4A1027378. H. Kim was supported by NRF-2020R1C1C1A01009760, J. Ok was supported by NRF-2017R1C1B2010328.

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Byun, SS., Kim, H. & Ok, J. Local Hölder continuity for fractional nonlocal equations with general growth. Math. Ann. 387, 807–846 (2023). https://doi.org/10.1007/s00208-022-02472-y

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