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Research Article | Open Access

Gradient estimates in generalized Orlicz spaces for quasilinear elliptic equations via extrapolation

Ruimin Wu1( ), Yinsheng Jiang2, Liyuan Wang3
Mathematics Teaching Department, Lanzhou Technology and Business College, Gansu, MO 730101, China
College of Mathematics and Systems Science, Xinjiang University, Urumqi, MO 830046, China
Lanzhou University of Technology, Lanzhou, MO 730050, China
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Abstract

The gradient estimates in the generalized Orlicz space for weak solutions of a class of quasi-linear elliptic boundary value problems are obtained using the modern technique of extrapolation. The coefficients are assumed to have small BMO seminorms, and the boundary of the domain is sufficiently flat in the sense of Reifenberg. As a corollary, we apply our results to the variable Lebesgue spaces.

Keywords

elliptic PDE of p-LaplacianReifenberg flat domaingeneralized Orlic spaceextrapolation
CLC number: 35R35, 42B20, 46E30

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AIMS Mathematics
Volume 8 Issue 10,
October 2023
Pages 24153-24161
DOI: 10.3934/math.20231231

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Cite this article:
Wu R, Jiang Y, Wang L. Gradient estimates in generalized Orlicz spaces for quasilinear elliptic equations via extrapolation. AIMS Mathematics, 2023, 8(10): 24153-24161. https://doi.org/10.3934/math.20231231

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Received: 22 April 2023
Revised: 26 July 2023
Accepted: 26 July 2023
Published: 15 October 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)