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Calderón–Zygmund Type Results for a Class of Quasilinear Elliptic Equations Involving the p(x)-Laplacian

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Abstract

In this study, we obtain global Calderón–Zygmund-type estimates for weak solutions to quasilinear elliptic equations driven by p(x)-Laplacian operator. We prove two results concerning both classical and generalized Lorentz spaces with two weights. Moreover, our interest in this paper is to estimate regularity estimates via fractional maximal operators and this tool is reminiscent of the idea described by Tran and Nguyen in (J. Funct. Anal. 280, 108797, 2021), (J. Differ. Equ. 268, 1427–1462, 2020), (J. Math. Anal. Appl. 509, 125928, 2022).

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Acknowledgements

This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.02-2021.17. The authors would like to thank Minh-Phuong Tran for her helpful inspiration, interesting discussions, and her constant encouragement for us in this research. Many thanks also to Thanh-Nhan Nguyen for his useful observations on a preliminary version of this paper. Also, we would like to thank the Editor(s) and Referee(s) for having investigated our manuscript, giving us critical remarks, as well as proposing helpful suggestions for improving our work.

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Authors and Affiliations

  1. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    My-Kim-An Tran

  2. Department of Mathematics, Ho Chi Minh City University of Education, Ho Chi Minh City, Vietnam

    Nhu-Y Truong

  3. Ho Chi Minh City University of Technology and Education, Ho Chi Minh City, Vietnam

    Huong-Lan Tran

  4. Nguyen Huu Huan High School, Thu Duc City, Vietnam

    The-Quang Tran

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  1. My-Kim-An Tran
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  2. Nhu-Y Truong
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  3. Huong-Lan Tran
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  4. The-Quang Tran
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Tran, MKA., Truong, NY., Tran, HL. et al. Calderón–Zygmund Type Results for a Class of Quasilinear Elliptic Equations Involving the p(x)-Laplacian. Vietnam J. Math. (2024). https://doi.org/10.1007/s10013-024-00690-2

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