Academic Journal
Weak and renormalized solutions for anisotropic Neumann problems with degenerate coercivity
| العنوان: | Weak and renormalized solutions for anisotropic Neumann problems with degenerate coercivity |
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| المؤلفون: | Benboubker, Mohamed Badr, Benkhalou, Hayat, Hjiaj, Hassane |
| المصدر: | Boletim da Sociedade Paranaense de Matemática; Vol 41 (2023); 1-25 ; Boletim da Sociedade Paranaense de Matemática; v. 41 (2023); 1-25 ; 2175-1188 ; 0037-8712 |
| بيانات النشر: | Sociedade Paranaense de Matemática |
| سنة النشر: | 2022 |
| المجموعة: | Universidade Estadual de Maringá: Portal de Periódicos da UEM |
| الوصف: | In this work, we study the following quasilinear Neumann boundary-value problem$$\left\{\begin{array}{ll}\displaystyle -\sum^{N}_{i=1} D^{i}(a_{i}(x,u,\nabla u))+|u|^{p_{0}-2} u= f(x,u,\nabla u) & \mbox{in } \ \quad \Omega,\\\displaystyle \sum^{N}_{i=1} a_{i}(x,u,\nabla u)\cdot n_{i} = g(x) & \mbox{on } \ \quad \partial\Omega,\end{array}\right.$$where $\Omega$ is a bounded open domain in $\>I\!\!R^{N}$, $(N\geq 2)$. We prove the existence of a weak solution for $f \in L^{\infty}(\Omega)$ and $g\in L^{\infty}(\partial\Omega)$ and the existence of renormalized solutions for $L^{1}$-data $f$ and $g$. The functional setting involves anisotropic Sobolev spaces with constants exponents. |
| نوع الوثيقة: | article in journal/newspaper |
| وصف الملف: | application/pdf |
| اللغة: | English |
| Relation: | http://eduemojs.uem.br/ojs/index.php/BSocParanMat/article/view/62362/751375155412; http://eduemojs.uem.br/ojs/index.php/BSocParanMat/article/view/62362 |
| DOI: | 10.5269/bspm.62362 |
| الاتاحة: | http://eduemojs.uem.br/ojs/index.php/BSocParanMat/article/view/62362 https://doi.org/10.5269/bspm.62362 |
| Rights: | Copyright (c) 2022 Boletim da Sociedade Paranaense de Matemática ; http://creativecommons.org/licenses/by/4.0 |
| رقم الانضمام: | edsbas.3FB199A5 |
| قاعدة البيانات: | BASE |
| DOI: | 10.5269/bspm.62362 |
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