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Gradient estimates for a class of quasilinear elliptic equations with measure data

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Abstract

We study a class of non-homogeneous quasilinear elliptic equations with measure data to obtain an optimal regularity estimate. We prove that the gradient of a weak solution to the problem is as integrable as the first order maximal function of the associated measure in the Orlicz spaces up to a correct power.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 11471207, 11571020 and 11671111) and Heilongjiang Province Postdoctoral Startup Foundation (Grant No. LBH- Q16082).

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Authors and Affiliations

  1. Department of Mathematics, Shanghai University, Shanghai, 200444, China

    Fengping Yao

  2. Department of Mathematics and Institute for Advanced Study in Mathematics, Harbin Institute of Technology, Harbin, 150001, China

    Chao Zhang

  3. LMAM, School of Mathematical Sciences, Peking University, Beijing, 100871, China

    Shulin Zhou

Authors
  1. Fengping Yao
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  2. Chao Zhang
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  3. Shulin Zhou
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Correspondence to Chao Zhang.

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Yao, F., Zhang, C. & Zhou, S. Gradient estimates for a class of quasilinear elliptic equations with measure data. Sci. China Math. 62, 1719–1730 (2019). https://doi.org/10.1007/s11425-017-9205-y

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  • DOI: https://doi.org/10.1007/s11425-017-9205-y

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