پیوندهای مفید
آمار
| تعداد نشریات | 22 |
| تعداد شمارهها | 709 |
| تعداد مقالات | 10,223 |
| تعداد مشاهده مقاله | 71,696,131 |
| تعداد دریافت فایل اصل مقاله | 63,514,751 |
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 | ||
|
[1] Y. Akdim, E. Azroul, and M.Rhoudaf, Existence of T-solution for degenerated problem via Minty’s Lemma, Acta Math. Sinica English Ser. 24 (2008),431–438. [2] O. Azraibi, B. El Haji, and M. Mekkour, Entropy solution for nonlinear elliptic boundary value problem having large monotonicity in Musielak-Orlicz-Sobolev spaces, Asia Pac. J. Math. 10 (2023), no. 7. [3] O. Azraibi, B. El Haji, and M. Mekkour, Nonlinear parabolic problem with lower order terms in Musielak-Sobolev spaces without sign condition and with Measure data, Palestine J. Math. 11 (2022), no. 3, 474–503. [4] O. Azraibi, B. EL haji, and M. Mekkour, On some nonlinear elliptic problems with large monotonicity in Musielak–Orlicz–Sobolev spaces, J. Math. Phys. Anal. Geom. 18 (2022), no. 3, 1-–18. [5] O. Azraibi, B. EL Haji, and M. Mekkour, Strongly nonlinear unilateral anisotropic elliptic problem with data, Asia Math. 7 (2023), no. 1, 1–20. [6] A. Benkirane and A. Elmahi, Almost everywhere convergence of the gradient of solutions to elliptic equations in Orlicz spaces, Nonlinear Anal. T.M.A. 28 (1997), no. 11, 1769–1784. [7] A. Benkirane, B. El Haji, and M. El Moumni, On the existence of solution for degenerate parabolic equations with singular terms, Pure Appl. Math. Quart. 14 (2018), no. 3-4, 591–606. [8] A. Benkirane, B. El Haji, and M. El Moumni, Strongly nonlinear elliptic problem with measure data in Musielak-Orlicz spaces, Complex Variab. Elliptic Equ. 67 (2022), no. 6, 1447–1469. [9] A. Benkirane, B. El Haji, and M. El Moumni, On the existence solutions for some nonlinear elliptic problem, Bol. Soc. Paran. Mat. (3s.) 40 (2022), 1–8. [10] A. Benkirane, N. El Amarty, B. El Haji, and M. El Moumni, Existence of solutions for a class of nonlinear elliptic problems with measure data in the setting of Musielak–Orlicz–Sobolev spaces, J. Elliptic Parabol. Equ. 9 (2023), 647–672. [11] L. Boccardo, Some nonlinear Dirichlet problems in L1 involving lower order terms in divergence form, Prog. Elliptic Parabolic Partial Differ. Equ. 350 (1996), 43–57. [12] Y. Chen, S. Levine, and M. Rao, Variable exponent, linear growth functionals in image restoration SIAM J. Appl. Math. 66 (2006), 1383–1406. [13] J. Droniou and A. Prignet, Equivalence between entropy and renormalized solutions for parabolic equations with smooth measure data, NoDEA Nonlinear Differ. Equ. Appl. 14 (2007) no. 1-2, 181–205. [14] B. El Haji and M. El Moumni, and A. Talha, Entropy solutions for nonlinear parabolic equations in Musielak Orlicz spaces without Delta2-conditions, Gulf J. Math. 9 (2020), Issue 1, 1–26. [15] B. El Haji and M. El Moumni, Entropy solutions of nonlinear elliptic equations with L1-data and without strict monotonicity conditions in weighted Orlicz-Sobolev spaces, J. Nonlinear Funct. Anal. 2021 (2021), Article ID 8, 1–17. [16] B. El Haji, M. El Moumni, and K. Kouhaila, On a nonlinear elliptic problems having large monotonicity with L1-data in weighted Orlicz-Sobolev spaces, Moroccan J. Pure Appl. Anal. 5 (2021), 104–116. [17] B. El Haji and M. El Moumni, and K. Kouhaila, Existence of entropy solutions for nonlinear elliptic problem having large monotonicity in weighted Orlicz-Sobolev spaces, LE Math. 76 (2021), no. 1, 37–61. [18] B. El Haji, M. El Moumni, and A. Talha, Entropy Solutions of Nonlinear Parabolic Equations in Musielak Framework Without Sign Condition and L1-Data Asian J. Math. Appl. 2021 (2021), Article ID ama0575. [19] N. El Amarty, B. El Haji and M. El Moumni, Entropy solutions for unilateral parabolic problems with L1-data in Musielak-Orlicz-Sobolev spaces, Palestine J. Math. 11 (2022), no. 1, 504–523. [20] N. El Amarty, B. El Haji, and M. El Moumni, Existence of renormalized solution for nonlinear elliptic boundary value problem without Δ2-condition, SeMA 77 (2020), 389–414. [21] I. Fragal`a, F. Gazzola, and B. Kawohl, Existence and nonexistence results for anisotropic quasilinear elliptic equations, Ann. Inst. H. Poincare Anal. Non Lineaire 21 (2004), 715–734. [22] L.F.O. Faria, O.H. Miyagaki, D. Motreanub, and M. Tanaka, Existence results for nonlinear elliptic equations with Leray-Lions operator and dependence on the gradient, Nonlinear Anal. 96 (2014), 154–166. [23] J.-P. Gossez and V. Mustonen, Variational inequalities in Orlicz-Sobolev spaces, Nonlinear Anal. 11 (1987), no. 3, 379–392. [24] E. Hewitt and K. Stromberg, Real and Abstract Analysis, Springer-Verlag, Berlin Heidelberg New York, 1965. [25] M. Mihailescu, P. Pucci, and V. Radulescu, Eigenvalue problems for anisotropic quasilinear elliptic equations with variable exponent, J. Math. Anal. Appl. 340 (2008), 687–698. [26] M. Troisi, Teoremi di inclusione per spazi di Sobolev non isotropi, Ricerche Mat. 18 (1969), 3–24. [27] F. Petitta, A.C. Ponce, and A. Porretta, Diffuse measures and nonlinear parabolic equations, J. Evol. Equ. 11 (2011), no. 4, 861–905. [28] F. Petitta, Asymptotic behavior of solutions for parabolic operators of Leray-Lions type and measure data, Adv. Differ. Equ. 12 (2007), no. 8, 867–891. [29] A. Prignet, Existence and uniqueness of ”entropy”, solutions of parabolic problems with L1 data, Nonlinear Anal. 28 (1997) no. 12, 1943–1954. [30] A. Porretta and S. Segura de Leon; Nonlinear elliptic equations having a gradient term with natural growth, J. Math. Pures Appl. 85 (2006), no. 3, 465–492. [31] A. Razani, Nonstandard competing anisotropic (p; q)-Laplacians with convolution, Boundary Value Prob. 2022 (2022), 87. [32] A. Razani, Entire weak solutions for an anisotropic equation in the Heisenberg group, Proc. Amer. Math. Soc. 151 (2023), no. 11, 47714779. [33] A. Razani, G.S. Costa, and G. M. Figueiredo, A positive solution for a weighted anisotropic p-Laplace equation involving vanishing potential, Mediterr. J. Math. 21 (2024), no. 2, 59. [34] A. Razani and G.M. Figueiredo, Existence of infinitely many solutions for an anisotropic equation using genus theory, Math. Meth. Appl. Sci. 45 (2022), no. 12, 7591–7606. [35] A. Razani and G.M. Figueiredo, Degenerated and competing anisotropic (p; q)-Laplacians with weights, Appl. Anal. 102 (2023), no. 16, 4471–4488. [36] A. Razani and G.M. Figueiredo, A positive solution for an anisotropic p&q-Laplacian, Discrete Continuous Dyn. Syst. Ser. S 16 (2023), no. 6, 16291643. [37] A. Razani and G.M. Figueiredo, Positive solutions for a semipositone anisotropic p-Laplacian problem, Boundary Value Prob. 2024 (2024), no. 1, 34. [38] T. Soltani and A. Razani, Solutions for an anisotropic elliptic problem involving nonlinear terms, Q. Math. 47 (2024), no. 1, 93–112. [39] W. Rudin, Real and Complex Analysis, 3rd ed., McGraw-Hill, New York, 1974. [40] V. Zhikov, Averaging of functionals in the calculus of variations and elasticity, Math. USSR Izv. 29 (1987), 33–66 | ||
|
آمار تعداد مشاهده مقاله: 1,057 تعداد دریافت فایل اصل مقاله: 767 |
||