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Potential estimates for elliptic measure data problems with irregular obstacles

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Abstract

We study nonlinear elliptic obstacle problems of p-Laplacian type when the right-hand side is a bounded Borel measure. We prove pointwise gradient estimates for solutions in terms of potentials under a minimal assumption on the obstacle.

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Acknowledgements

The authors would like to thank the referee for careful reading of the manuscript and giving valuable comments.

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Authors and Affiliations

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

    Sun-Sig Byun

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

    Kyeong Song

  3. Department of Mathematics, Yeungnam University, Gyeongsan, 38541, Korea

    Yeonghun Youn

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  1. Sun-Sig Byun
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  2. Kyeong Song
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  3. Yeonghun Youn
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Correspondence to Kyeong Song.

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This work was supported by National Research Foundation of Korea Grant (NRF-2021R1A4A1027378).

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Byun, SS., Song, K. & Youn, Y. Potential estimates for elliptic measure data problems with irregular obstacles. Math. Ann. 387, 745–805 (2023). https://doi.org/10.1007/s00208-022-02471-z

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