| Title:
|
Existence of weak solutions for elliptic Dirichlet problems with variable exponent (English) |
| Author:
|
Kim, Sungchol |
| Author:
|
Ri, Dukman |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
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2464-7136 (online) |
| Volume:
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148 |
| Issue:
|
3 |
| Year:
|
2023 |
| Pages:
|
283-302 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper presents several sufficient conditions for the existence of weak solutions to general nonlinear elliptic problems of the type $$ \begin{cases} -{\rm div} a(x, u, \nabla u)+b(x, u, \nabla u)=0 &\text {in} \ \Omega ,\\ u=0 &\text {on} \ \partial \Omega , \end{cases} $$ where $\Omega $ is a bounded domain of $\mathbb R^n$, $n\ge 2$. In particular, we do not require strict monotonicity of the principal part $a(x,z,\cdot )$, while the approach is based on the variational method and results of the variable exponent function spaces. (English) |
| Keyword:
|
variable exponent |
| Keyword:
|
existence |
| Keyword:
|
variational methods |
| Keyword:
|
Dirichlet problem |
| MSC:
|
35J20 |
| MSC:
|
35J25 |
| MSC:
|
35J70 |
| idZBL:
|
Zbl 07729578 |
| idMR:
|
MR4628614 |
| DOI:
|
10.21136/MB.2022.0069-21 |
| . |
| Date available:
|
2023-08-11T14:13:27Z |
| Last updated:
|
2023-09-13 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151760 |
| . |
| Reference:
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