An existence and approximation theorem for solutions of degenerate nonlinear elliptic equations

Albo Carlos Cavalheiro

Abstract


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

Keywords


Degenerate nonlinear elliptic equations; weighted Sobolev spaces

Full Text:

PDF

References


Cavalheiro, A. C., An approximation theorem for solutions of degenerate elliptic equations, Proc. Edinb. Math. Soc. 45 (2002), 363-389.

Fabes, E., Kenig, C., Serapioni, R., The local regularity of solutions of degenerate elliptic equations, Comm. Partial Differential Equations 7 (1982), 77-116.

Fernandes, J. C., Franchi, B., Existence and properties of the Green function for a class of degenerate parabolic equations, Rev. Mat. Iberoam. 12 (1996), 491-525.

Garcıa-Cuerva, J., Rubio de Francia, J. L., Weighted Norm Inequalities and Related Topics, North-Holland Publishing Co., Amsterdam, 1985.

Heinonen, J., Kilpelainen, T., Martio, O., Nonlinear Potential Theory of Degenerate Elliptic Equations, Oxford University Press, Oxford, 1993.

Kufner, A., Weighted Sobolev Spaces, John Wiley & Sons, New York, 1985.

Muckenhoupt, B., Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207-226.

Murthy, M. K. V., Stampacchia, G., Boundary value problems for some degenerate elliptic operators, Ann. Mat. Pura Appl. 80 (1) (1968), 1-122.

Torchinsky, A., Real-Variable Methods in Harmonic Analysis, Academic Press, San Diego, 1986.

Turesson, B. O., Nonlinear Potential Theory and Weighted Sobolev Spaces, Springer-Verlag, Berlin, 2000.

Zeidler, E., Nonlinear Functional Analysis and Its Applications. Vol. II/B, Springer-Verlag, New York, 1990.




DOI: http://dx.doi.org/10.17951/a.2018.72.1.29-43
Data publikacji: 2018-06-25 09:04:04
Data złożenia artykułu: 2018-06-24 16:51:39

Refbacks

  • There are currently no refbacks.


Copyright (c) 2018 Albo Carlos Cavalheiro