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Communications in Mathematics

Editor-in-Chief: Rossi, Olga

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Mathematical Citation Quotient (MCQ) 2016: 0.28

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2336-1298
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An approximation theorem for solutions of degenerate semilinear elliptic equations

Albo Carlos Cavalheiro
Published Online: 2017-06-28 | DOI: https://doi.org/10.1515/cm-2017-0004

Abstract

The main result establishes that a weak solution of degenerate semilinear elliptic equations can be approximated by a sequence of solutions for non-degenerate semilinear elliptic equations.

Keywords: Degenerate semilinear elliptic equations; weighted Sobolev Spaces

References

  • [1] A. C. Cavalheiro: An approximation theorem for solutions of degenerate elliptic equations. Proc. Edinb. Math. Soc. 45 (2002) 363{389. doi:CrossrefGoogle Scholar

  • [2] A. C. Cavalheiro: Existence of solutions in weighted Sobolev spaces for some degenerate semilinear elliptic equations. Appl. Math. Lett. 17 (2004) 387{391. doi:CrossrefGoogle Scholar

  • [3] A. C. Cavalheiro: Existence results for the Dirichlet problem of some degenerate nonlinear elliptic equations. J. Appl. Anal. 20 (2) (2014) 145{154. doi:CrossrefGoogle Scholar

  • [4] A. C. Cavalheiro: Uniqueness of solutions for some degenerate nonlinear elliptic equations. Appl. Math. (Warsaw) 41 (1) (2014) 93{106.Google Scholar

  • [5] A. C. Cavalheiro: Existence and uniqueness of solutions for the Navier problems with degenerate nonlinear elliptic equations. Note Mat. 25 (2) (2015) 1{16.Google Scholar

  • [6] E. Fabes, C. Kenig, R. Serapioni: The local regularity of solutions of degenerate elliptic equations. Comm. Partial Di erential Equations 7 (1982) 77{116. doi:CrossrefGoogle Scholar

  • [7] J. C. Fernandes, B. Franchi: Existence and properties of the Green function for a class of degenerate parabolic equations. Rev. Mat. Iberoam. 12 (1996) 491{525.CrossrefGoogle Scholar

  • [8] J. Garcia-Cuerva, J. L. Rubio de Francia: Weighted Norm Inequalities and Related Topics. North-Holland Mathematics Studies 116 (1985).Google Scholar

  • [9] J. Heinonen, T. Kilpeläinen, O. Martio: Nonlinear Potential Theory of Degenerate Elliptic Equations. Oxford Math. Monographs, Clarendon Press (1993).Google Scholar

  • [10] A. Kufner: Weighted Sobolev Spaces. John Wiley & Sons, New York (1985).Web of ScienceGoogle Scholar

  • [11] B. Muckenhoupt: Weighted norm inequalities for the Hardy maximal function. Trans. Amer. Math. Soc. 165 (1972) 207{226.Google Scholar

  • [12] A. Torchinsky: Real-Variable Methods in Harmonic Analysis. Academic Press, San Diego (1986).Google Scholar

  • [13] B. O. Turesson: Nonlinear Potential Theory and Weighted Sobolev Spaces. Springer-Verlag (2000). Lecture Notes in Math.Google Scholar

About the article

Received: 2016-11-16

Accepted: 2017-03-16

Published Online: 2017-06-28

Published in Print: 2017-06-27


Citation Information: Communications in Mathematics, ISSN (Online) 2336-1298, DOI: https://doi.org/10.1515/cm-2017-0004.

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© 2017. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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