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Existence and uniqueness of solutions for some degenerate nonlinear Dirichlet problems

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Języki publikacji
EN
Abstrakty
EN
In this work we are interested in the existence of solutions for the Dirichlet problem associated with the degenerate nonlinear elliptic equations -∑ni,j=1Djij(x)Diu(x))+b(x)u(x)+div(Φ(u(x)))=g(x)-∑nj=1fj(x) on Ω in the setting of the weighted Sobolev spaces W1,p0(Ω, ω).
Wydawca
Rocznik
Strony
41--54
Opis fizyczny
Bibliogr. 16 poz.
Twórcy
  • Department of Mathematics, State University of Londrina, Londrina, PR 86057-970, Brazil
Bibliografia
  • [1] A. C. Cavalheiro, Existence results for degenerate quasilinear elliptic equations in weighted Sobolev spaces, Bull. Belg. Math. Soc. Simon Stevin 17 (2010), 141-153.
  • [2] A. C. Cavalheiro, A theorem on global regularity for solutions of degenerate elliptic equations, Comm. Math. Anal. 11 (2011), 1-12.
  • [3] E. Fabes, C. Kenig and R. Serapioni, The local regularity of solutions of degenerate elliptic equations, Comm. Partial Differential Equations 7 (1982), 77-116.
  • [4] B. Franchi and R. Serapioni, Pointwise estimates for a class of strongly degenerate elliptic operators: A geometrical approach, Ann. Scuola Norm. Sup. Pisa 14 (1987), 527-568.
  • [5] J. Garcia-Cuerva and J. L. Rubio de Francia, Weighted Norm Inequalities and Related Topics, North-Holland Math. Stud. 116, North-Holland, Amsterdam, 1985.
  • [6] D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, Berlin, 1977.
  • [7] J. Heinonen, T. Kilpeläinen and O. Martio, Nonlinear Potential Theory of Degenerate Elliptic Equations, Oxford Math. Monogr., Clarendon Press, 1993.
  • [8] D. Kinderlehrer and G. Stampacchia, An Introduction to Variational Inequalities and their Applications, Academic Press, New York, 1980.
  • [9] A. Kufner, Weighted Sobolev Spaces, John Wiley & Sons, 1985.
  • [10] A. Kufner and B. Opic, Hardy-Type Inequalities, Pitman Research Notes in Mathematics Series 219, Longman Scientific & Technical, Harlow, 1990.
  • [11] B. Muckenhoupt, Weighted norm inequalities for the Hardy maximal function, Trans. Am. Math. Soc. 165 (1972), 207-226.
  • [12] A. Porretta, Uniqueness of solutions for some nonlinear Dirichlet problems, Nonlinear Diff. Equ. Appl. 11 (2004), 407-430.
  • [13] G. Stampacchia, Equations elliptiques du second ordre à coefficients discontinus, Séminaires de Mathématiques Supérieures 16, Presses de l’Université de Montréal, Montréal, 1966.
  • [14] E. Stein, Harmonie Analysis, Princeton University Press, 1993.
  • [15] A. Torchinsky, Real-Variable Methods in Harmonie Analysis, Academic Press, San Diego, 1986.
  • [16] B. O. Turesson, Nonlinear Potential Theory and Weighted Sobolev Spaces, Lecture Notes in Math. 1736, Springer, 2000.
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Bibliografia
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bwmeta1.element.baztech-c8fd8526-5675-4505-8968-d17867ab6a9c
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