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On some anisotropic elliptic problem with measure data | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 1، دوره 16، شماره 5، مرداد 2025، صفحه 1-11 اصل مقاله (432.7 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2024.33483.4992 | ||
| نویسندگان | ||
| Ouidad Azraibia1؛ Derham Abdelkarim2؛ Badr El Haji* 2 | ||
| 1Laboratory LAMA, Department of Mathematics, Faculty of Sciences Dhar El Mahraz, Sidi Mohammed Ben Abdallah University, PB 1796 Fez-Atlas, Fez, Morocco | ||
| 2Laboratory LaR2A, Departement of Mathematics, Faculty of Sciences Tetouan, Abdelmalek Essaadi University, BP 2121, Tetouan, Morocco | ||
| تاریخ دریافت: 20 بهمن 1402، تاریخ بازنگری: 28 اسفند 1402، تاریخ پذیرش: 29 اسفند 1402 | ||
| چکیده | ||
| We prove optimal existence results for entropy solutions to some anisotropic boundary value problems like \begin{equation}\label{pro} \left\{\begin{array}{lll} -\sum_{i=1}^N D^i A_i(x, w, \nabla w)= f-\operatorname{div} F(w) \textrm{ in }\Omega, & \textrm{in }&\Omega, \\ v=0 & \textrm{on } &\partial \Omega, \end{array}\right. \end{equation} where $ f \in L^{1}(\Omega) $, $ F = (F_{1}, . . . , F_{N}) $ satisfies $ F \in (C^{0}(\mathbb{R}))^{N}. $and $\Omega $ is a bounded, open subset of ${\mathbb{R}^{N}}$, $ N\geq 2$, and the function $A_{i}(x, s, \xi)$ verify the large monotonicity condition. The construction of the proof of our theorem is done by using Minty's Lemma in its modified version. | ||
| کلیدواژهها | ||
| Entropy solutions؛ nonlinear elliptic equations, anisotropic Sobolev spaces, entropy solutions | ||
| مراجع | ||
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