Existence of renormalized solutions for some degenerate and non-coercive elliptic equations
This paper is devoted to the study of some nonlinear degenerated elliptic equations, whose prototype is given by \alignat2&-{\rm div}( b(|u|)|\nabla u|^{p-2}\nabla u) + d(|u|)|\nabla u|^p = f - {\rm div}(c(x)|u|^{\alpha}) &\quad&in \Omega, & u = 0 &\quad&on \partial\Omeg...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Institute of Mathematics of the Czech Academy of Science
2023-07-01
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| Series: | Mathematica Bohemica |
| Subjects: | |
| Online Access: | http://mb.math.cas.cz/full/148/2/mb148_2_9.pdf |
| _version_ | 1827957887026069504 |
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| author | Youssef Akdim Mohammed Belayachi Hassane Hjiaj |
| author_facet | Youssef Akdim Mohammed Belayachi Hassane Hjiaj |
| author_sort | Youssef Akdim |
| collection | DOAJ |
| description | This paper is devoted to the study of some nonlinear degenerated elliptic equations, whose prototype is given by
\alignat2&-{\rm div}( b(|u|)|\nabla u|^{p-2}\nabla u) + d(|u|)|\nabla u|^p = f - {\rm div}(c(x)|u|^{\alpha}) &\quad&in \Omega,
& u = 0 &\quad&on \partial\Omega,
where $\Omega$ is a bounded open set of $\mathbb{R}^N$ ($N\geq2$) 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 $L^{\frc{N}{(p-1)}}(\Omega).$ We show the existence of renormalized solutions for this non-coercive elliptic equation, also, some regularity results will be concluded. |
| first_indexed | 2024-04-09T15:27:06Z |
| format | Article |
| id | doaj.art-89e0274dfcb54ebf9c6acdab595126fd |
| institution | Directory Open Access Journal |
| issn | 0862-7959 2464-7136 |
| language | English |
| last_indexed | 2024-04-09T15:27:06Z |
| publishDate | 2023-07-01 |
| publisher | Institute of Mathematics of the Czech Academy of Science |
| record_format | Article |
| series | Mathematica Bohemica |
| spelling | doaj.art-89e0274dfcb54ebf9c6acdab595126fd2023-04-28T12:19:41ZengInstitute of Mathematics of the Czech Academy of ScienceMathematica Bohemica0862-79592464-71362023-07-01148225528210.21136/MB.2022.0061-21MB.2022.0061-21Existence of renormalized solutions for some degenerate and non-coercive elliptic equationsYoussef AkdimMohammed BelayachiHassane HjiajThis paper is devoted to the study of some nonlinear degenerated elliptic equations, whose prototype is given by \alignat2&-{\rm div}( b(|u|)|\nabla u|^{p-2}\nabla u) + d(|u|)|\nabla u|^p = f - {\rm div}(c(x)|u|^{\alpha}) &\quad&in \Omega, & u = 0 &\quad&on \partial\Omega, where $\Omega$ is a bounded open set of $\mathbb{R}^N$ ($N\geq2$) 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 $L^{\frc{N}{(p-1)}}(\Omega).$ We show the existence of renormalized solutions for this non-coercive elliptic equation, also, some regularity results will be concluded.http://mb.math.cas.cz/full/148/2/mb148_2_9.pdf renormalized solution nonlinear elliptic equation non-coercive problem |
| spellingShingle | Youssef Akdim Mohammed Belayachi Hassane Hjiaj Existence of renormalized solutions for some degenerate and non-coercive elliptic equations Mathematica Bohemica renormalized solution nonlinear elliptic equation non-coercive problem |
| title | Existence of renormalized solutions for some degenerate and non-coercive elliptic equations |
| title_full | Existence of renormalized solutions for some degenerate and non-coercive elliptic equations |
| title_fullStr | Existence of renormalized solutions for some degenerate and non-coercive elliptic equations |
| title_full_unstemmed | Existence of renormalized solutions for some degenerate and non-coercive elliptic equations |
| title_short | Existence of renormalized solutions for some degenerate and non-coercive elliptic equations |
| title_sort | existence of renormalized solutions for some degenerate and non coercive elliptic equations |
| topic | renormalized solution nonlinear elliptic equation non-coercive problem |
| url | http://mb.math.cas.cz/full/148/2/mb148_2_9.pdf |
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