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Irregular Double Obstacle Problems with Orlicz Growth

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Abstract

We study an irregular double obstacle problem with Orlicz growth over a nonsmooth bounded domain. We establish a global Calderón–Zygmund estimate by proving that the gradient of the solution to such a nonlinear elliptic problem is as integrable as both the nonhomogeneous term in divergence form and the gradient of the associated double obstacles. We also investigate minimal regularity requirements on the relevant nonlinear operator for the desired regularity estimate.

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Acknowledgements

S. Byun was supported by NRF-2017R1A2B2003877. J. Ok was supported by NRF-2017R1C1B2010328. L. Shuang was partially supported by NRF-2015R1A4A1041675.

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Authors and Affiliations

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

    Sun-Sig Byun

  2. Department of Mathematics, Beijing Jiaotong University, Beijing, 100044, China

    Shuang Liang

  3. Department of Applied Mathematics and the Institute of Natural Sciences, Kyung Hee University, Yongin, 17104, Republic of Korea

    Jihoon Ok

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  1. Sun-Sig Byun
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  2. Shuang Liang
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  3. Jihoon Ok
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Correspondence to Sun-Sig Byun or Jihoon Ok.

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Byun, SS., Liang, S. & Ok, J. Irregular Double Obstacle Problems with Orlicz Growth. J Geom Anal 30, 1965–1984 (2020). https://doi.org/10.1007/s12220-020-00352-y

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