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Global Boundedness of Weak Solutions to Fractional Nonlocal Equations

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  • Zhenjie Li

    (School of Mathematical Sciences, Guangxi Minzu University, Nanning 530006, China
    School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China)

  • Lihe Wang

    (School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
    Department of Mathematics, University of Iowa, Iowa City, IA 52242-1419, USA)

  • Chunqin Zhou

    (School of Mathematical Sciences, CMA-Shanghai, Shanghai Jiao Tong University, Shanghai 200240, China)

Abstract

In this paper, we establish the global boundedness of weak solutions to fractional nonlocal equations using the fractional Moser iteration argument and some other ideas. Our results not only extend the boundedness result of Ros-Oton-Serra to general fractional nonlocal equations under a weaker assumption can but also be viewed as a generalization of the boundedness of weak solutions of second-order elliptic equations to nonlocal equations.

Suggested Citation

  • Zhenjie Li & Lihe Wang & Chunqin Zhou, 2025. "Global Boundedness of Weak Solutions to Fractional Nonlocal Equations," Mathematics, MDPI, vol. 13(16), pages 1-14, August.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:16:p:2612-:d:1724874
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