86
Views
0
CrossRef citations to date
0
Altmetric
Research Article

Variable exponents anisotropic nonlinear elliptic systems with Lp′→(⋅)-data

Received 24 Nov 2023, Accepted 22 Jun 2024, Published online: 03 Jul 2024

References

  • Zhikov VV. Averaging of functionals of the calculus of variations and elasticity theory. Math USSR Izv. 1987;29:33–66. doi: 10.1070/IM1987v029n01ABEH000958
  • Zhikov VV. On passing to the limit in nonlinear variational problem. Math Sb. 1992;183:47–84.
  • Zhikov VV, Kozlov SM, Oleinik OA. Homogenization of differential operators and integral functionals. Berlin: Springer-Verlag; 1994.
  • Zhikov VV. On Lavrentiev's phenomenon. Russ J Math Phys. 1995;3:249–269.
  • Alkhutov YA, Zhikov VV. Existence and uniqueness theorems for solutions of parabolic equations with a variable nonlinearity exponent. Math Sb. 2014;205(3):3–14. doi: 10.4213/sm
  • Alkhutov YA, Zhikov VV. Existence theorems for solutions of parabolic equations with variable order of nonlinearity. Proc Steklov Inst Math. 2010;270:21–32. doi: 10.1134/S0081543810030028
  • Alkhutov YA, Krasheninnikova OV. On the continuity of solutions to elliptic equations with variable order of nonlinearity. Proc Steklov Inst Math. 2008;261:1–10. doi: 10.1134/S0081543808020016
  • Alkhutov YA, Zhikov VV. Hölder continuity of solutions of parabolic equations with variable nonlinearity exponent. J Math Sci. 2011;179:347–389. doi: 10.1007/s10958-011-0599-9
  • Mihailescu M, Radulescu V. A multiplicity result for a nonlinear degenerate problem arising in the theory of electrorheological fluids. Proc R Soc A. 2006;462:2625–2641. doi: 10.1098/rspa.2005.1633
  • Ružička M. Electrorheological fluids: modeling and mathematical theory. In: Lecture Notes in Mathematics, 1748, Berlin: Springer; 2000.
  • Chen Y, Levine S, Rao M. Variable exponent, linear growth functionals in image restoration. SIAM J Appl Math. 2006;66:1383–1406. doi: 10.1137/050624522
  • Naceri M, Mokhtari F. Anisotropic nonlinear elliptic systems with variable exponents and degenerate coercivity. Appl Anal. 2021;100(11):2347–2367. doi: 10.1080/00036811.2019.1682136
  • Allaoui NE, Mokhtari F. Anisotropic elliptic system with variable exponents and degenerate coercivity with Lm data. Appl Anal. 2023;103:1241–1261. doi: 10.1080/00036811.2023.2240333
  • Naceri M, Benboubker MB. Distributional solutions of anisotropic nonlinear elliptic systems with variable exponents: existence and regularity. Adv Oper Theory. 2022;7(2):1–34.
  • Naceri M. Anisotropic nonlinear elliptic systems with variable exponents, degenerate coercivity and Lq(⋅) data. Ann Acad Rom Sci Ser Math Appl. 2022;14:107–140.
  • Bendahmane M, Mokhtari F. Nonlinear elliptic systems with variable exponents and measure data. Moroccan J Pure Appl Anal. 2015;1:108–125. doi: 10.7603/s40956-015-0008-3
  • Bendahmane M, Karlsen KH. Anisotropic nonlinear elliptic systems with measure data and anisotropic harmonic maps into spheres. Electr J Differ Equ. 2006;2006(46):1–30.
  • Dolzmann G, Hungerbuhler N, Muller S. Non-linear elliptic systems with measure-valued right hand side. Math Z. 1997;226:545–574. doi: 10.1007/PL00004354
  • Fan X, Zhao D. On the spaces Lp(x)(Ω) and W1,p(x)(Ω). J Math Anal Appl. 2001;263:424–446. doi: 10.1006/jmaa.2000.7617
  • Cruz-Uribe D, Fiorenza A, Ruzhansky M, et al. Variable Lebesgue spaces and hyperbolic systems. In: Advanced Courses in Mathematics -- CRM Barcelona. Basel: Birkhäuser; 2014.
  • Diening L, Harjulehto P, Hästö P, et al. Lebesgue and Sobolev spaces with variable exponents. In: Lecture Notes in Mathematics. Vol. 2017, New York: Springer; 2011.
  • Fan X. Anisotropic variable exponent Sobolev spaces and p→(x)-Laplacian equations. Complex Var Elliptic Equ. 2011;56:623–642. doi: 10.1080/17476931003728412
  • Karlsen KH (CMA). Notes on weak convergence (MAT4380 -- Spring 2006), 2006.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.