Glasnik Matematicki, Vol. 57, No. 1 (2022), 35-47. \( \)

HÖLDER CONTINUITY FOR THE SOLUTIONS OF THE \(p(x)\)-LAPLACE EQUATION WITH GENERAL RIGHT-HAND SIDE

Abdeslem Lyaghfouri

Department of Mathematical Sciences, United Arab Emirates University, Al Ain, Abu Dhabi, UAE
e-mail:a.lyaghfouri@uaeu.ac.ae

Abstract.   We show that bounded solutions of the quasilinear elliptic equation \(\Delta_{p(x)} u=g+div(\textbf{F})\) are locally Hölder continuous provided that the functions \(g\) and \(\textbf{F}\) are in suitable Lebesgue spaces.

2020 Mathematics Subject Classification.   35B65, 35J92

Key words and phrases.   \(p(x)\)-Laplacian, Hölder continuity

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https://doi.org/10.3336/gm.57.1.03

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