Global Boundedness of Weak Solutions to Fractional Nonlocal Equations

Zhenjie Li (), Lihe Wang and Chunqin Zhou
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Zhenjie Li: School of Mathematical Sciences, Guangxi Minzu University, Nanning 530006, China
Lihe Wang: School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
Chunqin Zhou: School of Mathematical Sciences, CMA-Shanghai, Shanghai Jiao Tong University, Shanghai 200240, China

Mathematics, 2025, vol. 13, issue 16, 1-14

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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