Publication Cover
Applicable Analysis
An International Journal
Volume 103, 2024 - Issue 7
135
Views
0
CrossRef citations to date
0
Altmetric
Research Article

Anisotropic elliptic system with variable exponents and degenerate coercivity with Lm data

&
Pages 1241-1261 | Received 02 Jun 2023, Accepted 19 Jul 2023, Published online: 28 Jul 2023

References

  • Ruzicka M. Ectrorheological fluids: modeling and mathematical theory. Berlin: Springer; 2000. (Lecture Notes in Mathematics; vol. 1748). doi: 10.1007/BFb0104029
  • Pfeiffer C, Mavroidis C, Bar-Cohen Y, et al. Electrorheological fluid based force feedback device. In Proc 1999 SPIE Telemanipulator and Telepresence Technologies VI Conf (Boston, MA); 1999; Vol. 3840. p. 88–99.
  • 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
  • Zhikov VV. Averaging of functionals of the calculus of variations and elasticity theory. Math USSR-Izvestiya. 1987;29:33–66. doi: 10.1070/IM1987v029n01ABEH000958
  • Troisi M. Teoremi di inclusione per spazi di sobolev non isotropi. Ric Mat. 1969;XVIII:3–24.
  • Boccardo L, Dall'Aglio A, Orsina L. Existence and regularity results for some elliptic equations with degenerate coercivity. Atti Semin Mat Fis Univ Modena Reggio Emilia. 1998;46:51–81.
  • Gao H, Leonetti F, Ren W. Regularity for anisotropic elliptic equations with degenerate coercivity. Nonlinear Anal. 2019;187:493–505. doi: 10.1016/j.na.2019.06.017
  • Leonetti F, Schianchi R. A remark on some degenerate elliptic problems. Ann Univ Ferrara – Sez VII – Sc Mat. 1998;44:123–128. doi: 10.1007/BF02828019
  • Ayadi H, Mokhtari F. Nonlinear anisotropic elliptic equations with variable exponents and degenerate coercivity. Elec J Differ Equ. 2018;2018:1–23. doi: 10.1186/s13662-017-1452-3
  • Croce G. The regularizing effects of some lower order terms in an elliptic equation with degenerate coercivity. Red Mat Appl. 2007;27:299–314. doi: 10.48550/arXiv.1005.0203
  • Giachetti D, Porzio MM. Elliptic equations with degenerate coercivity:gradient regularity. Acta Math Sin English Ser. 2003;19(2):349–370. doi: 10.1007/s10114-002-0235-1
  • Leonetti F, Schianchi RA. Remark on some degenerate elliptic problems. Ann Univ Ferrara – Sez VII – Sc Mat. 1998;44:123–128. doi: 10.1007/BF02828019
  • Dyda B. Fractional calculus for power functions and eigenvalues of the fractional laplacian. Fract Calcu Appl Anal. 2012;15(4):536–555. doi: 10.2478/s13540-012-0038-8
  • Guariglia E. Fractional calculus, zeta functions and Shannon entropy. Open Mathe. 2021;19(1):87–100. doi: 10.1515/math-2021-0010
  • Ragusa MA. Commutators of fractional integral operators on Vanishing-Morrey spaces. J Glob Optim. 2008;40(1-3):361–368. doi: 10.1007/s10898-007-9176-7
  • Guariglia E. Riemann zeta fractional derivative–functional equation and link with primes. Adv Differ Equ. 2019;2019(1):261. doi: 10.1186/s13662-019-2202-5
  • Ragusa MARA, Safari F. Existence of radial solutions for a p(x)-Laplacian dirichlet problem. Adv Differ Equ. 2021;2021:215. doi: 10.1186/s13662-021-03369-x
  • Necas J, Stara J. Principio di massimo per i sistemi ellittici quasi-lineari non diagonali. Boll Unione Mat Ital. 1972;6(4):1–10.
  • Yan ZQ. Everywhere regularity for solutions to quasilinear elliptic systems of triangular form. In: Partial differential equations(Tianjin, 1986), Lecture Notes in Math. 1306. Berlin: Springer; 1988. p. 255–261.
  • Leonetti F, Rocha E, Staicu V. Quasilinear elliptic systems with measure data. Nonlinear Anal Theory Methods Appl. 2017;154:210–224. doi: 10.1016/j.na.2016.04.002
  • Leonetti F, Rocha E, Staicu V. Smallness and cancellation in some elliptic systems with measure data. J Math Anal Appl. 2018;465:885–902. doi: 10.1016/j.jmaa.2018.05.047
  • Dolzmann G, Hungerbühler N, Müller S. The p-harmonic system with measure valued right hand side. Analyses De L'I H P Section C. 1997;14:353–364. doi: 10.1016/S0294-1449(97)80141-2
  • Leonetti F, Petricca PV. Anisotropic elliptic systems with measure data. Ric Di Math. 2005;54(2):591–595.
  • Leonetti F, Petricca PV. Existence for some vectorial elliptic problems with measure data. Riv Mat Univ Parma. 2006;05:33–46.
  • Geo H, Huang M, Deng H, et al. Global integrability for solutions to quasilinear elliptic systems. Spr-Verl GmbH Germany. 2020;164:23–37. doi: 10.1007/s00229-020-01183-5
  • Zhou S. A note on nonlinear elliptic systems involving measures. Elect J Diff Equ. 2000;2000:1–6.
  • Bendahmane M, Karlsen KH. Anisotropic nonlinear elliptic systems with measure data and anisotropic harmonic maps into spheres. Elect J Diff Equ. 2006;2006:1–30.
  • Allaoui NE, Mokhtari F. Anisotropic nonlinear elliptic system With degenerate coercivity and Lm data. J Math Inequa. 2023.
  • Gao H, Liang S, Cui Y. Regularity for anisotropic solutions to some nonlinear elliptic system. Front Math China. 2016;11:77–87. doi: 10.1007/s11464-015-0443-5
  • Mokhtar N, Mokhtari F. Anisotropic nonlinear elliptic systems with variable exponents and degenerate coercivity. Appl Anal. 2021;100:2347–2367. doi: 10.1080/00036811.2019.1682136
  • Diening L, Harjulehto P, Hästö P, et al. Lebesgue and sobolev spaces with variable exponents. New York: Springer; 2011. (Lecture Notes in Mathematics; 2017).
  • Edmunds DE, Rakosnik J. Sobolev embeddings with variable exponent. II Math Nachr. 2002;53-67:246–247. doi: 10.1002/1522-2616(200212)246:1<53::AID-MANA53>3.0.CO;2-T
  • Fan X. Anisotropic variable exponent sobolev spaces and p→(x)-Laplacian equations. Complex Var Elliptic Equ. 2010;15:1–20. doi: 10.1080/17476931003728412
  • Mokhtari F. Anisotropic parabolic problems with measures data. Differ Equ Appl. 2010;2(1):123–150. doi: 10.7153/dea-02-09
  • Dolzmann G, Hungerbühler N, Müller S. Uniqueness and maximal regularity for nonlinear elliptic systems of n-Laplace type with measure valued right hand side. J Reine Angew Math. 2000:1–35. doi: 10.1515/crll.2000.022
  • Dolzmann G, Hungerbuhler N, Muller S. Nonlinear elliptic systems with measure valued right hande side. Math Z. 1997;226:545–574. doi: 10.1007/PL00004354
  • Bendahmane M, Karlsen KH, Saad M. Nonlinear anisotropic elliptic and parabolic equation with variable exponents and L1 data. Pure Appl Anal. 2013;12:1201–1220. doi: 10.3934/cpaa.2013.12.1201
  • Mokhtari F. Regularity of the solution to nonlinear anisotropic elliptic equations with variable exponents and irregular data. Mediterr J Math. 2017;17:14:141. doi: 10.1007/s00009-017-0941-7
  • Sanchón M, Urbano M. Entropy solutions for the p(x)-Laplace equation. Trans Amer Math Soc. 2009;361:6387–6405. doi: 10.1090/S0002-9947-09-04399-2
  • Lions JL. Quelques méthodes de résolution des problémes aux limites non linéaires. Dunod; 1969.
  • Bendahmane M, Mokhtari F. Nonlinear elliptic systems with variable exponents and measure data. Moroccan J Pure Appl Anal (MJPAA). 2015;1(2):108–125. doi: 10.7603/s40956-015-0008-3

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.