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Global \(W^{1,p}\) regularity for elliptic problem with measure source and Leray–Hardy potential

Ricerche di Matematica (2022)Cite this article

Abstract

In this paper, we develop the Littman–Stampacchia–Weinberger duality approach to obtain global \(W^{1,p}\) estimates for a class of elliptic problems involving Leray–Hardy operators and measure sources in a distributional framework associated to a dual formulation with a specific weight function.

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Acknowledgements

H. Chen is supported by the Natural Science Foundation of China, No. 12071189, by Jiangxi Province Science Fund for Distinguished Young Scholars, No. 20212ACB211005, and by the Jiangxi Provincial Natural Science Foundation, No. 20202ACBL201001, by the Science and Technology Research Project of Jiangxi Provincial Department of Education, No. GJJ200307, GJJ200325.

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Authors and Affiliations

  1. Department of Mathematics, Jiangxi Normal University, Nanchang, 330022, China

    Huyuan Chen

  2. California State University, Los Angeles, 5151, USA

    Hichem Hajaiej

Authors
  1. Huyuan Chen
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  2. Hichem Hajaiej
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Correspondence to Hichem Hajaiej.

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Chen, H., Hajaiej, H. Global \(W^{1,p}\) regularity for elliptic problem with measure source and Leray–Hardy potential. Ricerche mat (2022). https://doi.org/10.1007/s11587-021-00615-y

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  • DOI: https://doi.org/10.1007/s11587-021-00615-y

Keywords

  • Leray–Hardy potential
  • Duality approach
  • Radon measure

Mathematics Subject Classification

  • 35J75
  • 35B99
  • 35D99