| Title:
|
Existence of renormalized solutions for some degenerate and non-coercive elliptic equations (English) |
| Author:
|
Akdim, Youssef |
| Author:
|
Belayachi, Mohammed |
| Author:
|
Hjiaj, Hassane |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
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148 |
| Issue:
|
2 |
| Year:
|
2023 |
| Pages:
|
255-282 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper is devoted to the study of some nonlinear degenerated elliptic equations, whose prototype is given by $$ \begin{aligned}t 2&-{\rm div}( b(|u|)|\nabla u|^{p-2}\nabla u) + d(|u|)|\nabla u|^{p} = f - {\rm div}(c(x)|u|^{\alpha }) &\quad &\mbox {in}\ \Omega ,\\ & u = 0 &\quad &\mbox {on}\ \partial \Omega , \end{aligned}t $$ where $\Omega $ is a bounded open set of $\mathbb {R}^N$ ($N\geq 2$) with $1<p<N$ and $f \in L^{1}(\Omega ),$ under some growth conditions on the function $b(\cdot )$ and $d(\cdot ),$ where $c(\cdot )$ is assumed to be in $L^{\frac {N}{(p-1)}}(\Omega ).$ We show the existence of renormalized solutions for this non-coercive elliptic equation, also, some regularity results will be concluded. (English) |
| Keyword:
|
renormalized solution |
| Keyword:
|
nonlinear elliptic equation |
| Keyword:
|
non-coercive problem |
| MSC:
|
35J60 |
| MSC:
|
46E30 |
| MSC:
|
46E35 |
| idZBL:
|
Zbl 07729577 |
| idMR:
|
MR4585581 |
| DOI:
|
10.21136/MB.2022.0061-21 |
| . |
| Date available:
|
2023-05-04T18:00:48Z |
| Last updated:
|
2023-09-13 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151689 |
| . |
| Reference:
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