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

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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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