Gradient estimate of a variable power for nonlinear elliptic equations with Orlicz growth
In this paper, we prove a global Calderón-Zygmund type estimate in the framework of Lorentz spaces for a variable power of the gradients to the zero-Dirichlet problem of general nonlinear elliptic equations with the nonlinearities satisfying Orlicz growth. It is mainly assumed that the variable expo...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2020-07-01
|
| Series: | Advances in Nonlinear Analysis |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/anona-2020-0121 |
| id |
doaj-fbbef6e8e2454a6f98a352b4cc8a0e03 |
|---|---|
| record_format |
Article |
| spelling |
doaj-fbbef6e8e2454a6f98a352b4cc8a0e032021-09-06T19:39:56ZengDe GruyterAdvances in Nonlinear Analysis2191-94962191-950X2020-07-0110117219310.1515/anona-2020-0121anona-2020-0121Gradient estimate of a variable power for nonlinear elliptic equations with Orlicz growthLiang Shuang0Zheng Shenzhou1Department of Mathematics, Beijing Jiaotong University, Beijing, 100044, ChinaDepartment of Mathematics, Beijing Jiaotong University, Beijing, 100044, ChinaIn this paper, we prove a global Calderón-Zygmund type estimate in the framework of Lorentz spaces for a variable power of the gradients to the zero-Dirichlet problem of general nonlinear elliptic equations with the nonlinearities satisfying Orlicz growth. It is mainly assumed that the variable exponents p(x) satisfy the log-Hölder continuity, while the nonlinearity and underlying domain (A, Ω) is (δ, R0)-vanishing in x ∈ Ω.https://doi.org/10.1515/anona-2020-0121nonlinear elliptic equationsorlicz growthlorentz estimate of the variable powerlog-hölder continuity(δ, r0)-vanishing of (a, ω)35j6035b65 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Liang Shuang Zheng Shenzhou |
| spellingShingle |
Liang Shuang Zheng Shenzhou Gradient estimate of a variable power for nonlinear elliptic equations with Orlicz growth Advances in Nonlinear Analysis nonlinear elliptic equations orlicz growth lorentz estimate of the variable power log-hölder continuity (δ, r0)-vanishing of (a, ω) 35j60 35b65 |
| author_facet |
Liang Shuang Zheng Shenzhou |
| author_sort |
Liang Shuang |
| title |
Gradient estimate of a variable power for nonlinear elliptic equations with Orlicz growth |
| title_short |
Gradient estimate of a variable power for nonlinear elliptic equations with Orlicz growth |
| title_full |
Gradient estimate of a variable power for nonlinear elliptic equations with Orlicz growth |
| title_fullStr |
Gradient estimate of a variable power for nonlinear elliptic equations with Orlicz growth |
| title_full_unstemmed |
Gradient estimate of a variable power for nonlinear elliptic equations with Orlicz growth |
| title_sort |
gradient estimate of a variable power for nonlinear elliptic equations with orlicz growth |
| publisher |
De Gruyter |
| series |
Advances in Nonlinear Analysis |
| issn |
2191-9496 2191-950X |
| publishDate |
2020-07-01 |
| description |
In this paper, we prove a global Calderón-Zygmund type estimate in the framework of Lorentz spaces for a variable power of the gradients to the zero-Dirichlet problem of general nonlinear elliptic equations with the nonlinearities satisfying Orlicz growth. It is mainly assumed that the variable exponents p(x) satisfy the log-Hölder continuity, while the nonlinearity and underlying domain (A, Ω) is (δ, R0)-vanishing in x ∈ Ω. |
| topic |
nonlinear elliptic equations orlicz growth lorentz estimate of the variable power log-hölder continuity (δ, r0)-vanishing of (a, ω) 35j60 35b65 |
| url |
https://doi.org/10.1515/anona-2020-0121 |
| work_keys_str_mv |
AT liangshuang gradientestimateofavariablepowerfornonlinearellipticequationswithorliczgrowth AT zhengshenzhou gradientestimateofavariablepowerfornonlinearellipticequationswithorliczgrowth |
| _version_ |
1717769741197639680 |