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Article

Global Boundedness of Weak Solutions to Fractional Nonlocal Equations

1
School of Mathematical Sciences, Guangxi Minzu University, Nanning 530006, China
2
School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
3
Department of Mathematics, University of Iowa, Iowa City, IA 52242-1419, USA
4
School of Mathematical Sciences, CMA-Shanghai, Shanghai Jiao Tong University, Shanghai 200240, China
*
Author to whom correspondence should be addressed.
Mathematics 2025, 13(16), 2612; https://doi.org/10.3390/math13162612
Submission received: 29 June 2025 / Revised: 29 July 2025 / Accepted: 6 August 2025 / Published: 14 August 2025

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.
Keywords: fractional nonlocal equations; fractional Sobolev inequality; Moser iterations fractional nonlocal equations; fractional Sobolev inequality; Moser iterations

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MDPI and ACS Style

Li, Z.; Wang, L.; Zhou, C. Global Boundedness of Weak Solutions to Fractional Nonlocal Equations. Mathematics 2025, 13, 2612. https://doi.org/10.3390/math13162612

AMA Style

Li Z, Wang L, Zhou C. Global Boundedness of Weak Solutions to Fractional Nonlocal Equations. Mathematics. 2025; 13(16):2612. https://doi.org/10.3390/math13162612

Chicago/Turabian Style

Li, Zhenjie, Lihe Wang, and Chunqin Zhou. 2025. "Global Boundedness of Weak Solutions to Fractional Nonlocal Equations" Mathematics 13, no. 16: 2612. https://doi.org/10.3390/math13162612

APA Style

Li, Z., Wang, L., & Zhou, C. (2025). Global Boundedness of Weak Solutions to Fractional Nonlocal Equations. Mathematics, 13(16), 2612. https://doi.org/10.3390/math13162612

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