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Regularity in Orlicz spaces for the Poisson equation

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Abstract

In this paper, we establish a regularity theory in the Orlicz space for the Poisson equation −Δu = f, where f lies in the Orlicz space \(L^{\phi}\) with \(\phi\) satisfying Δ2 and ∇2 conditions. The proof is based on standard W 2, p estimates and Hardy–Littlewood maximal functions.

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Authors and Affiliations

  1. Department of Mathematics, Xi’an Jiaotong University, Xi’an, 710049, China

    Huilian Jia, Dongsheng Li & Lihe Wang

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  1. Huilian Jia
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  2. Dongsheng Li
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  3. Lihe Wang
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Correspondence to Huilian Jia.

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Jia, H., Li, D. & Wang, L. Regularity in Orlicz spaces for the Poisson equation. manuscripta math. 122, 265–275 (2007). https://doi.org/10.1007/s00229-006-0066-y

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  • DOI: https://doi.org/10.1007/s00229-006-0066-y

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