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Existence and uniqueness of weak solution in weighted Sobolev spaces for a class of nonlinear degenerate elliptic problems with measure data | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 215، دوره 13، شماره 1، خرداد 2022، صفحه 2635-2653 اصل مقاله (400.09 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.23603.2564 | ||
| نویسندگان | ||
| Mohamed El Ouaarabi* ؛ Adil Abbassi؛ Chakir Allalou | ||
| Laboratory LMACS, FST of Beni Mellal, BP 523, 23000, Sultan Moulay Slimane University, Morocco | ||
| تاریخ دریافت: 15 خرداد 1400، تاریخ بازنگری: 02 شهریور 1400، تاریخ پذیرش: 08 آبان 1400 | ||
| چکیده | ||
| In this paper, we study the existence and uniqueness of weak solution to a Dirichlet boundary value problems for the following nonlinear degenerate elliptic problems \begin{equation*} -{\rm{div}}\Big[ \omega_{1}\mathcal{A}(x,\nabla u)+\nu_{2}\mathcal{B}(x,u,\nabla u)\Big]+ \nu_{1}\mathcal{C}(x,u)+ \omega_{2}\vert u\vert^{p-2}u=f-{\rm{div}}F, \end{equation*} where $1 < p < \infty$, $\omega_{1}$, $\nu_{2}$, $\nu_{1}$ and $\omega_{2}$ are $A_p$-weight functions, and $\mathcal{A}:\Omega\times \mathbb{R}^n\longrightarrow\mathbb{R}^n$, $\mathcal{B}:\Omega\times\mathbb{R}\times \mathbb{R}^n\longrightarrow\mathbb{R}^n$, $\mathcal{C}:\Omega\times\mathbb{R}\longrightarrow\mathbb{R}$ are Carat'eodory functions that satisfy some conditions and the right-hand side term $f-{\rm{div}}F$ belongs to $L^{p'}(\Omega,\omega_{2}^{1-p'})+\prod\limits_{j=1}^{n}L^{p'}(\Omega,\omega_{1}^{1-p'})$. We will use the Browder-Minty Theorem and the weighted Sobolev spaces theory to prove the existence and uniqueness of weak solution in the weighted Sobolev space $W^{1,p}_ 0(\Omega,\omega_1,\omega_{2})$. | ||
| کلیدواژهها | ||
| Dirichlet problem؛ nonlinear degenerate elliptic problems؛ Browder-Minty Theorem؛ weighted Sobolev spaces؛ weak solution | ||
| مراجع | ||
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