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International Journal of Differential Equations
Volume 2011 (2011), Article ID 356356, 17 pages
doi:10.1155/2011/356356
Research Article

𝐿 ∞ -Solutions for Some Nonlinear Degenerate Elliptic Equations

Albo Carlos Cavalheiro

Department of Mathematics, State University of Londrina, 86051-990 Londrina, PR, Brazil

Received 17 May 2011; Revised 6 October 2011; Accepted 6 October 2011

Academic Editor: Toka Diagana

Copyright © 2011 Albo Carlos Cavalheiro. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. C. Cavalheiro, β€œExistence results for degenerate quasilinear elliptic equations in weighted Sobolev spaces,” Bulletin of the Belgian Mathematical Society. Simon Stevin, vol. 17, no. 1, pp. 141–153, 2010. View at Zentralblatt MATH
  2. P. Drábek, A. Kufner, and V. Mustonen, β€œPseudo-monotonicity and degenerated or singular elliptic operators,” Bulletin of the Australian Mathematical Society, vol. 58, no. 2, pp. 213–221, 1998. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  3. E. Fabes, C. Kenig, and R. Serapioni, β€œThe local regularity of solutions of degenerate elliptic equations,” Communications in Partial Differential Equations, vol. 7, no. 1, pp. 77–116, 1982. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  4. J. Heinonen, T. Kilpeläinen, and O. Martio, Nonlinear Potential Theory of Degenerate Elliptic Equations, Oxford Mathematical Monographs, The Clarendon Press, New York, NY, USA, 1993.
  5. B. Muckenhoupt, β€œWeighted norm inequalities for the Hardy maximal function,” Transactions of the American Mathematical Society, vol. 165, pp. 207–226, 1972. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  6. E. Stein, Harmonic Analysis, vol. 43, Princeton University Press, Princeton, NJ, USA, 1993.
  7. A. Torchinsky, Real-Variable Methods in Harmonic Analysis, vol. 123, Academic Press, San Diego, Calif, USA, 1986.
  8. A. Kufner, Weighted Sobolev Spaces, John Wiley & Sons, New York, NY, USA, 1985.
  9. L. Boccardo, F. Murat, and J.-P. Puel, β€œL∞-estimate for some nonlinear elliptic partial differential equations and application to an existence result,” SIAM Journal on Mathematical Analysis, vol. 23, no. 2, pp. 326–333, 1992. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  10. L. Boccardo, F. Murat, and J.-P. Puel, β€œExistence of bounded solutions for nonlinear elliptic unilateral problems,” Annali di Matematica Pura ed Applicata, vol. 152, pp. 183–196, 1988. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  11. J. Leray and J.-L. Lions, β€œQuelques résulatats de Višik sur les problèmes elliptiques nonlinéaires par les mèthodes de Minty-Browder,” Bulletin de la Sociètè Mathèmatique de France, vol. 93, pp. 97–107, 1965.
  12. J. García-Cuerva and J. L. Rubio de Francia, Weighted Norm Inequalities and Related Topics, vol. 116, North-Holland Mathematics Studies, Amsterdam, The Netherlands, 1985.
  13. B. O. Turesson, Nonlinear Potential Theory and Weighted Sobolev Spaces, vol. 1736 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 2000. View at Publisher Β· View at Google Scholar
  14. G. Stampacchia, Èquations Elliptiques du Second ordre à Coefficients Discontinus, Séminaire de Mathématiques Supérieures, Les Presses de l'Université de Montréal, Montreal, Quebec, 1966.
  15. E. Zeidler, Nonlinear Functional Analysis and Its Applications, vol. II/B, Springer, New York, NY, USA, 1990.