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Toward Weighted Lorentz–Sobolev Capacities from Caffarelli–Silvestre Extensions

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Abstract

Getting inspired by the Caffarelli–Silvestre extensions, this paper investigates the weighted Lorentz–Sobolev capacities and their capacitary strong inequalities with applications to the Sobolev-type embeddings. Consequently, the weighted Lebesgue-Sobolev capacities and their applications to a functional inequality problem and the existence-regularity of solutions to the prototype p-Laplace equations with weight are addressed as well.

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Authors and Affiliations

  1. Hubei Key Laboratory of Applied Mathematics, Faculty of Mathematics and Statistics, Hubei University, Wuhan, 430062, China

    Xing Fu

  2. Department of Mathematics and Statistics, Memorial University, St. John’s, NL, A1C 5S7, Canada

    Jie Xiao

  3. School of Mathematics, Southwest Jiaotong University, Chengdu, 610031, Sichuan, People’s Republic of China

    Qi Xiong

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  1. Xing Fu
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  2. Jie Xiao
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  3. Qi Xiong
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Correspondence to Qi Xiong.

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This project was completed during the research stays of the 1st & 3rd authors under supervision of the 2nd author at Memorial University with the support of: National Natural Science Foundation of China (Grant Nos. 11701160, 11871100, 12071229); NSERC of Canada (#202979); MUN’s SBM-Fund (#214311); Tianjin postgraduate research and innovation project (Grant No. 2021YJSB016); China Scholarship Council (Grant Nos. 202108420099, 202006200119).

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Fu, X., Xiao, J. & Xiong, Q. Toward Weighted Lorentz–Sobolev Capacities from Caffarelli–Silvestre Extensions. J Geom Anal 34, 124 (2024). https://doi.org/10.1007/s12220-024-01569-x

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