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

Ruimin Wu; Yinsheng Jiang; Liyuan Wang; Ruimin Wu; Yinsheng Jiang; Liyuan Wang

doi:10.3934/math.20231231

AIMS Mathematics

2023, Volume 8, Issue 10: 24153-24161. doi: 10.3934/math.20231231

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Research article

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

1.
Mathematics Teaching Department, Lanzhou Technology and Business College, Gansu, MO 730101, China
2.
College of Mathematics and Systems Science, Xinjiang University, Urumqi, MO 830046, China
3.
Lanzhou University of Technology, Lanzhou, MO 730050, China

Received: 22 April 2023 Revised: 26 July 2023 Accepted: 26 July 2023 Published: 10 August 2023
MSC : 35R35, 42B20, 46E30

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.
- elliptic PDE of $ p $-Laplacian,
- Reifenberg flat domain,
- generalized Orlic space,
- extrapolation
Citation: Ruimin Wu, Yinsheng Jiang, Liyuan Wang. Gradient estimates in generalized Orlicz spaces for quasilinear elliptic equations via extrapolation[J]. AIMS Mathematics, 2023, 8(10): 24153-24161. doi: 10.3934/math.20231231

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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.

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