On strongly quasilinear elliptic systems with weak monotonicity

References

[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. 10.5802/ambp.166Search in Google Scholar

[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. Search in Google Scholar

[3] E. Azroul and F. Balaadich, A weak solution to quasilinear elliptic problems with perturbed gradient, Rend. Circ. Mat. Palermo (2) (2020), 10.1007/s12215-020-00488-4. 10.1007/s12215-020-00488-4Search in Google Scholar

[4] E. Azroul and F. Balaadich, Quasilinear elliptic systems in perturbed form, Int. J. Nonlinear Anal. Appl. 10 (2019), no. 2, 255–266. Search in Google Scholar

[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. 10.1515/mjpaa-2018-0008Search in Google Scholar

[6] E. Azroul, A. Benkirane and O. Filali, Strongly nonlinear degenerated unilateral problems with L1 data, 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. Search in Google Scholar

[7] J. M. Ball, A version of the fundamental theorem for Young measures, PDEs and Continuum Models of Phase Transitions (Nice 1988), Lecture Notes in Phys. 344, Springer, Berlin (1989), 207–215. 10.1007/BFb0024945Search in Google Scholar

[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. Search in Google Scholar

[9] J. Chabrowski and K. Zhang, Quasi-monotonicity and perturbated systems with critical growth, Indiana Univ. Math. J. 41 (1992), no. 2, 483–504. 10.1512/iumj.1992.41.41028Search in Google Scholar

[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. 10.1016/S0362-546X(96)00317-3Search in Google Scholar

[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. 10.1007/PL00004354Search in Google Scholar

[12] G. B. Folland, Real Analysis, 2nd ed., John Wiley & Sons, New York, 1999. Search in Google Scholar

[13] P. Hess, A strongly nonlinear elliptic boundary value problem, J. Math. Anal. Appl. 43 (1973), 241–249. 10.1016/0022-247X(73)90272-2Search in Google Scholar

[14] N. Hungerbühler, A refinement of Ball’s theorem on Young measures, New York J. Math. 3 (1997), 48–53. Search in Google Scholar

[15] N. Hungerbühler, Quasilinear elliptic systems in divergence form with weak monotonicity, New York J. Math. 5 (1999), 83–90. Search in Google Scholar

[16] R. Landes, On Galerkin’s method in the existence theory of quasilinear elliptic equations, J. Funct. Anal. 39 (1980), no. 2, 123–148. 10.1016/0022-1236(80)90009-9Search in Google Scholar

[17] R. Landes, On the existence of weak solutions of perturbated systems with critical growth, J. Reine Angew. Math. 393 (1989), 21–38. 10.1515/crll.1989.393.21Search in Google Scholar

[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. 10.1023/A:1002050303320Search in Google Scholar

[19] M. Valadier, A course on Young measures, Rend. Istit. Mat. Univ. Trieste 26 (1994), 349–394. Search in Google Scholar

[20] J. R. L. Webb, Boundary value problems for strongly nonlinear elliptic equations, J. Lond. Math. Soc. (2) 21 (1980), no. 1, 123–132. 10.1112/jlms/s2-21.1.123Search in Google Scholar

[21] K. Yosida, Functional Analysis, 6th ed., Grundlehren Math. Wiss. 123, Springer, Berlin, 1980. Search in Google Scholar

[22] E. Zeidler, Nonlinear Functional Analysis and its Applications. I, Springer, New York, 1986. 10.1007/978-1-4612-4838-5Search in Google Scholar