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Tytuł artykułu

On strongly quasilinear elliptic systems with weak monotonicity

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we prove existence results in the setting of Sobolev spaces for a strongly quasilinear elliptic system by means of Young measures and mild monotonicity assumptions.
Wydawca
Rocznik
Strony
153--162
Opis fizyczny
Bibliogr. 22 poz.
Twórcy
  • Faculty of Sciences Dhar El Mehraz, Sidi Mohammed Ben Abdellah University, B.P. 1796 Atlas, Fez, Morocco
  • Faculty of Sciences Dhar El Mehraz, Sidi Mohammed Ben Abdellah University, B.P. 1796 Atlas, Fez, Morocco
Bibliografia
  • [1] Y. Akdim, E. Azroul and A. Benkirane, Existence of solution for quasilinear degenerated elliptic unilateral problems, Ann. Math. Blaise Pascal 10 (2003), no. 1, 1-20.
  • [2] F. Augsburger and N. Hungerbühler, Quasilinear elliptic systems in divergence form with weak monotonicity and nonlinear physical data, Electron. J. Differential Equations 2004 (2004), Paper No. 144.
  • [3] E. Azroul and F. Balaadich, A weak solution to quasilinear elliptic problems with perturbed gradient, Rend. Circ. Mat. Palermo (2) (2020), DOI 10.1007/s12215-020-00488-4.
  • [4] E. Azroul and F. Balaadich, Quasilinear elliptic systems in perturbed form, Int. J. Nonlinear Anal. Appl. 10 (2019), no. 2, 255-266.
  • [5] E. Azroul and F. Balaadich, Weak solutions for generalized p-Laplacian systems via Young measures, Moroccan J. Pure Appl. Anal. 4 (2018), no. 2, 77-84.
  • [6] E. Azroul, A. Benkirane and O. Filali, Strongly nonlinear degenerated unilateral problems with L1 data, in: Proceedings of the 2002 Fez Conference on Partial Differential Equations, Electron. J. Differ. Equ. Conf. 9, Southwest Texas State University, San Marcos (2002), 49-64.
  • [7] J. M. Ball, A version of the fundamental theorem for Young measures, in: PDEs and Continuum Models of Phase Transitions (Nice 1988), Lecture Notes in Phys. 344, Springer, Berlin (1989), 207-215.
  • [8] H. Brézis and F. E. Browder, Strongly nonlinear elliptic boundary value problems, Ann. Sc. Norm. Super. Pisa Cl. Sci. (4) 5 (1978), no. 3, 587-603.
  • [9] J. Chabrowski and K. Zhang, Quasi-monotonicity and perturbated systems with critical growth, Indiana Univ. Math. J. 41 (1992), no. 2, 483-504.
  • [10] G. Dal Maso and F. Murat, Almost everywhere convergence of gradients of solutions to nonlinear elliptic systems, Nonlinear Anal. 31 (1998), no. 3-4, 405-412.
  • [11] G. Dolzmann, N. Hungerbühler and S. Müller, Non-linear elliptic systems with measure-valued right hand side, Math. Z. 226 (1997), no. 4, 545-574.
  • [12] G. B. Folland, Real Analysis, 2nd ed., John Wiley & Sons, New York, 1999.
  • [13] P. Hess, A strongly nonlinear elliptic boundary value problem, J. Math. Anal. Appl. 43 (1973), 241-249.
  • [14] N. Hungerbühler, A refinement of Ball’s theorem on Young measures, New York J. Math. 3 (1997), 48-53.
  • [15] N. Hungerbühler, Quasilinear elliptic systems in divergence form with weak monotonicity, New York J. Math. 5 (1999), 83-90.
  • [16] R. Landes, On Galerkin’s method in the existence theory of quasilinear elliptic equations, J. Funct. Anal. 39 (1980), no. 2, 123-148.
  • [17] R. Landes, On the existence of weak solutions of perturbated systems with critical growth, J. Reine Angew. Math. 393 (1989), 21-38.
  • [18] M. A. Sychev, Characterization of homogeneous gradient Young measures in case of arbitrary integrands, Ann. Sc. Norm. Super. Pisa Cl. Sci. (4) 29 (2000), no. 3, 531-548.
  • [19] M. Valadier, A course on Young measures, Rend. Istit. Mat. Univ. Trieste 26 (1994), 349-394.
  • [20] J. R. L. Webb, Boundary value problems for strongly nonlinear elliptic equations, J. Lond. Math. Soc. (2) 21 (1980), no. 1, 123-132.
  • [21] K. Yosida, Functional Analysis, 6th ed., Grundlehren Math. Wiss. 123, Springer, Berlin, 1980.
  • [22] E. Zeidler, Nonlinear Functional Analysis and its Applications. I, Springer, New York, 1986.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021)
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-cf92a609-d224-4bc8-925d-b2797b0af726
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