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Articles

Strongly nonlinear elliptic problem with measure data in Musielak-Orlicz spaces

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Pages 1447-1469 | Received 24 Jun 2020, Accepted 25 Jan 2021, Published online: 11 Feb 2021

References

  • Boccardo L. Some nonlinear Dirichlet problems in L1 involving lower order terms in divergence form. Progress in Elliptic and Parabolic Partial Differential Equations (Capri, 1994), Pitman Res. Notes Math. Ser., vol. 350, Longman, Harlow, 1996, 43–57.
  • Bénilan Ph., Boccardo L, Gallouët T, Gariepy R, Pierre M, Vázquez JL. An L1-theory of existence and uniqueness of solutions of nonlinear elliptic equations. Ann Scuola Norm Sup Pisa Cl Sci. 1995;4(2):241–273.
  • Leone C, Porretta A. Entropy solutions for nonlinear elliptic equations in L1. Nonlinear Anal. 1998;32(3):325–334.
  • Lions PL, Murat F. Sur les solutions d'equations elliptiques non linéaires, to appear in C. R. Acad. Sci. Paris.
  • DiPerna RJ, Lions P-L. On the Cauchy problem for Boltzmann equations: global existence and weak stability. Ann. Math. (2). 1989;130(2):321–366. .
  • Bendahmane M, Wittbold P. Renormalized solutions for nonlinear elliptic equations with variable exponents and L1 data. Nonlinear Anal. 2009;70(2):567–583.
  • Sanchón M, Urbano JM. Entropy solutions for the p(x)-Laplace equation. Trans Am Math Soc. 2009;361(12):6387–6405.
  • Gossez JP, Mustonen V. Variationnal inequalities in Orlicz-Sobolev spaces. Nonlinear Anal. 1987;11:317–492.
  • Benkirane A, Sidi El Vally M. Variational inequalities in Musielak-Orlicz-Sobolev spaces. Bull Belg Math Soc Simon Stevin. 2014;21(5):787–811.
  • El Amarti N, El Haji B, El Moumni M. Existence of renomalized solution for nonlinear elliptic boundary value problem without Δ2 -condition. SeMA. 2020;77(4):389–414.
  • Akdim Y, Belayachi M, El Moumni M. L∞-bounds of solutions for strongly nonlinear elliptic problems with two lower order terms. Anal Theory Appl. 2017;33(1):46–58.
  • Akdim Y, Benkirane A, Douiri SM, El Moumni M. On a quasilinear degenerated elliptic unilateral problems with L1 data. Rend Circ Mat Palermo, II. Ser. 2018;67(1):43–57.
  • Akdim Y, Benkirane A, El Moumni M. Solutions of nonlinear elliptic problems with lower order terms. Ann Funct Anal (AFA). 2015;6(1):34–53.
  • Akdim Y, Benkirane A, El Moumni M. Existence results for nonlinear elliptic problems with lower order terms. Int J Evol Equ (IJEE). 2014;8(4):1–20.
  • Akdim Y, Benkirane A, El Moumni M, Fri A. Strongly nonlinear variational parabolic initial-boundary value problems. Ann University of Craiova -- Mathematics and Computer Science Series. 2014;41(2):1–13.
  • Akdim Y, Benkirane A, El Moumni M, Redwane H. Existence of renormalized solutions for nonlinear parabolic equations. J Partial Differ Equ (JPDE). 2014;27(1):28–49.
  • Akdim Y, Benkirane A, El Moumni M, Redwane H. Existence of renormalized solutions for strongly nonlinear parabolic problems with measure data. Georgian Math J. 2016;23(3):303–321.
  • Akdim Y, El Moumni M, Salmani A. Existence results for nonlinear anisotropic elliptic equation. Adv Sci Technol Eng Syst J. 2017;2(5):160–166.
  • Benbernou S, Gala S, Ragusa MA. On the regularity criteria for the 3D mag-netohydrodynamic equations via two components in terms of BMO space. Math Methods Appl Sci. 2014;37(15):2320–2325.
  • Benkirane A, El Haji B, El Moumni M. On the existence of solution for degenerate parabolic equations with singular terms. Pure Appl Math Q. 2018;14(3–4):591–606.
  • Benkirane A, El Moumni M, Fri A. An approximation of Hedberg's type in Sobolev spaces with variable exponent and application. Chinese J Math. 2014;2014:1–7. Article ID 549051.
  • Benkirane A, El Moumni M, Fri A. Renormalized solution for strongly nonlinear elliptic problems with lower order terms and L1-data. Izvestiya RAN: Ser Mat. 2017;81(3):3–20.
  • Benkirane A, El Moumni M, Kouhaila K. Solvability of strongly nonlinear elliptic variational problems in weighted Orlicz–Sobolev spaces. SeMA J. 2020;77(2):119–142. 1–24.
  • Benkirane A, Sidi El Vally M. Some approximation properties in Musielak-Orlicz-Sobolev spaces. Thai J Math. 2012;10(2):371–381.
  • El Haji B, El Moumni and K. Kouhaila M. On a nonlinear elliptic problems having large monotonocity with L1−data in weighted Orlicz-Sobolev spaces. Moroccan J Pure Appl Anal (MJPAA). 2019;5(1):104–116.
  • El Moumni M. Entropy solution for strongly nonlinear elliptic problems with lower order terms and L1-data. Ann University of Craiova -- Math Comput Sci Ser. 2013;40(2):211–225.
  • El Moumni M. Renormalized solutions for strongly nonlinear elliptic problems with lower order terms and measure data in Orlicz-Sobolev spaces. Iran J Math Sci Inform. 2019;14(1):95–119.
  • DiPerna RJ, Lion P-L. Global weak solutions of Vlasov-Maxwell systems. Commun Pure Appl Math. 1989;42(6):729–757.
  • Ragusa MA, Scapellato A. Mixed Morrey spaces and their applications to partial differential equations. Nonlinear Anal-Theory Methods Appl. 2017;151:51–65.
  • Ragusa MA, Tachikawa A. Regularity for minimizers for functionals of double phase with variable exponents. Adv Nonlinear Anal. 2020;9(1):710–728.
  • Ruzicka M. Electrorheological fluids: modeling and mathematical theory. Berlin: Springer; 2000. (Lecture Notes in Mathematics, vol. 1748).
  • Musielak J. Modular spaces and Orlicz spaces. Lecture Notes in Math. 10341983.
  • Ait Khellou M, Benkirane A, Douiri SM. Some properties of Musielak spaces with only the log-Hölder continuity condition and application. Ann Funct Anal Tusi Mathematical Research Group (TMRG). 2020;11(4):1062–1080.
  • Porretta A. Existence results for strongly nonlinear parabolic equations via strong conver- gence of truncations. Annali di Matematica Pura ed Applicata. (IV). 1999;CLXXVII(1):143–172.
  • Hewitt E, Stromberg K. Real and abstract analysis. Berlin: Springer; 1965.
  • Elarabi R, Rhoudaf M, Sabiki H. Entropy solution for a nonlinear elliptic problem with lower order term in Musielak-Orlicz spaces. Ric Mat. 2017;67(2):549–579.
  • Rudin W. Real and complex analysis, 3rd ed.. New York: McGraw-Hill; 1974.
  • El Moumni M. Nonlinear elliptic equations without sign condition and L1-data in Musielak-Orlicz-Sobolev spaces. Acta Appl Math. 2019;159(1):95–117.
  • Benkirane A, Elmahi A. Almost everywhere convergence of gradients of solutions to elliptic equations in Orlicz spaces and application. Nonlinear Anal Theory Methods Appl. 1997;28:1769–1784.

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