El Ouaarabi, Mohamed, Abbassi, Adil, Allalou, Chakir. (1400). Existence and uniqueness of weak solution in weighted Sobolev spaces for a class of nonlinear degenerate elliptic problems with measure data. هنرهای کاربردی, 13(1), 2635-2653. doi: 10.22075/ijnaa.2021.23603.2564
Mohamed El Ouaarabi; Adil Abbassi; Chakir Allalou. "Existence and uniqueness of weak solution in weighted Sobolev spaces for a class of nonlinear degenerate elliptic problems with measure data". هنرهای کاربردی, 13, 1, 1400, 2635-2653. doi: 10.22075/ijnaa.2021.23603.2564
El Ouaarabi, Mohamed, Abbassi, Adil, Allalou, Chakir. (1400). 'Existence and uniqueness of weak solution in weighted Sobolev spaces for a class of nonlinear degenerate elliptic problems with measure data', هنرهای کاربردی, 13(1), pp. 2635-2653. doi: 10.22075/ijnaa.2021.23603.2564
El Ouaarabi, Mohamed, Abbassi, Adil, Allalou, Chakir. Existence and uniqueness of weak solution in weighted Sobolev spaces for a class of nonlinear degenerate elliptic problems with measure data. هنرهای کاربردی, 1400; 13(1): 2635-2653. doi: 10.22075/ijnaa.2021.23603.2564

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
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
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