Gradient estimates in generalized Orlicz spaces for quasilinear elliptic equations via extrapolation-Reference-Cited by-同舟云学术

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

Published:2023 Issue:10 Volume:8 Page:24153-24161
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Wu Ruimin¹,Jiang Yinsheng²,Wang Liyuan³

Affiliation:

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

Abstract

<abstract><p>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.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference28 articles.

1. Y. Ahmida, I. Chlebicka, P. Gwiazda, A. Youssfi, Gossez's approximation theorems in Musielak-Orlicz-Sobolev spaces, J. Funct. Anal., 275 (2018), 2538–2571. http://doi.org/10.1016/j.jfa.2018.05.015

2. P. Baroni, M. Colombo, G. Mingione, Regularity for general functionals with double phase, Calc. Var. Partial Differ. Equ., 57 (2018), 62. http://doi.org/10.1007/s00526-018-1332-z

3. S. Byun, J. Oh, Global gradient estimates for non-uniformly elliptic equations, Calc. Var. Partial Differ. Equ., 56 (2017), 46. http://doi.org/10.1007/s00526-017-1148-2

4. S. Byun, L. Wang, S. Zhou, Nonlinear elliptic equations with small $BMO$ coefficients in Reifenberg domains, J. Funct. Anal., 250 (2007), 167–196. http://doi.org/10.1016/j.jfa.2007.04.021

5. S. Byun, F. P. Yao, S. L. Zhou, Gradient estimates in Orlicz space for nonlinear elliptic equations, J. Funct. Anal., 255 (2008), 1851–1873. http://doi.org/10.1016/j.jfa.2008.09.007