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Global regularity for degenerate/singular parabolic equations involving measure data

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Abstract

We consider degenerate and singular parabolic equations with p-Laplacian structure in bounded nonsmooth domains when the right-hand side is a signed Radon measure with finite total mass. We develop a new tool that allows global regularity estimates for the spatial gradient of solutions to such parabolic measure data problems, by introducing the (intrinsic) fractional maximal function of a given measure.

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Acknowledgements

The authors thank an anonymous referee for valuable comments. The authors also thank Wontae Kim for a helpful comment on Lemma 4.2.

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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. Korea Institute for Advanced Study, Seoul, 02455, Republic of Korea

    Jung-Tae Park

  3. Department of Mathematics, Kyonggi University, Suwon, 16227, Republic of Korea

    Pilsoo Shin

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  1. Sun-Sig Byun
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  2. Jung-Tae Park
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  3. Pilsoo Shin
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Correspondence to Jung-Tae Park.

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Communicated by M. Struwe.

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S.-S. Byun was supported by NRF-2017R1A2B2003877. J.-T. Park was supported by NRF-2019R1C1C1003844. P. Shin was supported by NRF-2020R1I1A1A01066850.

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Byun, SS., Park, JT. & Shin, P. Global regularity for degenerate/singular parabolic equations involving measure data. Calc. Var. 60, 18 (2021). https://doi.org/10.1007/s00526-020-01906-2

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