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Entropy solutions for variable exponents nonlinear anisotropic elliptic equations with natural growth terms
Soluciones de entropía para ecuaciones elípticas anisotrópicas no lineales de exponente variable con términos de crecimiento natural
DOI:
https://doi.org/10.15446/recolma.v58n1.117442Schlagworte:
Nonlinear, elliptic equation, natural growth term, Anisotropic Sobolev spaces, Variable exponents, Entropy solution (en)ecuaciones no lineales, ecuación elíptica, término de crecimiento natural, espacios de Sobolev anisotrópicos, exponentes variables, soluciones de entropía (es)
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In this paper, we prove existence results for entropy solutions of a nonlinear boundary value problems represented by a class of nonlinear elliptic anisotropic equations with variable exponents and natural growth terms. The functional setting involves variable exponents anisotropic Sobolev spaces.
En este artículo, probamos la existencia de soluciones de entropía para problemas de frontera no lineales correspondientes a una clase de ecuaciones anisotr´ópicas elípticas no lineales con exponentes variables y términos
de crecimiento natural.
Literaturhinweise
[1] A. Abbassi, C. Allalou, and A. Kassidi, Existence of Entropy Solutions of the Anisotropic Elliptic Nonlinear Problem with Measure Data in Weighted Sobolev Space, Bol. Soc. Paran. Mat. 40 (2022), 1-22.
[2] E. Azroul, M. B. Benboubker, and M. Rhoudaf, Entropy solution for some p(x)−quasilinear problem with right-hand side measure, Afr. Diaspora J. Math. (N.S.) 13(2) (2012), no. 62, 23-44.
[3] M. B. Benboubker, E. H. Azroul, and B. Abdelkrim, Quasilinear elliptic problems with nonstandard growth, Electronic Journal of Differential Equations 2011 (2011), no. 62, 1-16.
[4] M. B. Benboubker, H. Hjiaj, and S. Ouaro, Entropy solutions to nonlinear elliptic anisotropic problem with variable exponent, Journal of Applied Analysis and Computation 4 (2014), no. 3, 245-270.
[5] L. Boccardo, Some nonlinear Dirichlet problems in L1(Ω) involving lower order terms in divergence form, Progress in elliptic and parabolic partial differential equations (Capri, 1994) Pitman Res. Notes Math. Ser. 350 (1996), 43-57.
[6] S. Buccheri, Gradient estimates for nonlinear elliptic equations with first order terms, manuscripta math. 165 (2021), 191-225.
[7] Y. Chen, S. Levine, and M. Rao, Variable exponent, linear growth functionals in image restoration, SIAM J. Appl. Math. 66 (2006), 1383-1406.
[8] D. Cruz-Uribe, A. Fiorenza, M. Ruzhansky, and J. Wirth, Variable lebesgue spaces and hyperbolic systems, Advanced Courses in Mathematics - CRM Barcelona. Birkh¨auser, Basel, 2014.
[9] L. Diening, P. Harjulehto, P. H¨ast¨o, and M. Ruzicka, Lebesgue and Sobolev Spaces with Variable Exponents, Lecture Notes in Mathematics, Springer. vol. 2017, New York, 2011.
[10] X. Fan, Anisotropic variable exponent Sobolev spaces and −→p (x)-Laplacian equations, Complex Var Elliptic Equ. 56 (2011), 623-642.
[11] X. Fan and D. Zhao, On the spaces Lp(x)(Ω) and Wm,p(x)(Ω), J. Math. Anal. Appl. 263 (2001), 424-446.
[12] J. L. Henry, J. Velin, I. P. Moussa, and J. Nagau, Adaptive Smoothing for Visual Improvement of Image Quality via the p(x)−Laplacian Operator Effects of the p(x)−Laplacian Smoothing Operator on Digital Image Restoration: Contribution to an Adaptive Control Criterion, Appl. Sci., 2023, 13(20).
[13] M. Mihailescu and V. Radulescu, A multiplicity result for a nonlinear degenrate problem arising in the theory of eletrorheological fluids, Proc. R. Soc. A 462 (2006), 2625-2641.
[14] M. Naceri, Anisotropic nonlinear elliptic systems with variable exponents, degenerate coercivity and Lq(·) data, Ann. Acad. Rom. Sci. Ser. Math. Appl. 14 (2022), no. 1-2, 107-140.
[15] , Anisotropic nonlinear elliptic equations with variable exponents and two weighted first order terms, Filomat 38 (2024), no. 3, 1043-1054.
[16] M. Naceri and M. B. Benboubker, Distributional solutions of anisotropic nonlinear elliptic systems with variable exponents: existence and regularity, Advances in Operator Theory 7 (2022), no. 2, 1-34.
[17] M. Naceri and F. Mokhtari, Anisotropic nonlinear elliptic systems with variable exponents and degenerate coercivity, Appl. Anal 100 (2021), no. 11, 2347-2367.
[18] A. Porretta, Some remarks on the regularity of solutions for a class of elliptic equations with measure data, Houston J. Math. 26 (2000), 183-213.
[19] M. Ruˇziˇcka, Electrorheological fluids: modeling and mathematical theory, Springer, Berlin. Lecture Notes in Mathematics, 1748, 2000.
[20] E. Zeidler, Nonlinear functional analysis and its applications, II, B. Nonlinear monotone operators. Translated from the German by the author and Leo F, Boron Springer-Verlag, New York, 1990.
