| Title:
|
An approximation theorem for solutions of degenerate semilinear elliptic equations (English) |
| Author:
|
Cavalheiro, Albo Carlos |
| Language:
|
English |
| Journal:
|
Communications in Mathematics |
| ISSN:
|
1804-1388 |
| Volume:
|
25 |
| Issue:
|
1 |
| Year:
|
2017 |
| Pages:
|
21-34 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Degenerate semilinear elliptic equations |
| Keyword:
|
weighted Sobolev Spaces. |
| MSC:
|
35D30 |
| MSC:
|
35J61 |
| MSC:
|
35J70 |
| idZBL:
|
Zbl 1391.35141 |
| idMR:
|
MR3667074 |
| . |
| Date available:
|
2017-09-01T12:13:26Z |
| Last updated:
|
2020-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146842 |
| . |
| Reference:
|
[1] Cavalheiro, A. C.: An approximation theorem for solutions of degenerate elliptic equations.Proc. Edinb. Math. Soc., 45, 2002, 363-389, doi: 10.1017/S0013091500000079. Zbl 1195.35021, MR 1912646, 10.1017/S0013091500000079 |
| Reference:
|
[2] Cavalheiro, A. C.: Existence of solutions in weighted Sobolev spaces for some degenerate semilinear elliptic equations.Appl. Math. Lett., 17, 2004, 387-391, doi:10.1016/S0893-9659(04)00043-6. Zbl 1133.35351, MR 2045742, 10.1016/S0893-9659(04)90079-1 |
| Reference:
|
[3] Cavalheiro, A. C.: Existence results for the Dirichlet problem of some degenerate nonlinear elliptic equations.J. Appl. Anal., 20, 2, 2014, 145-154, doi:10.1515/jaa-2014-0016. Zbl 1305.35076, MR 3284721, 10.1515/jaa-2014-0016 |
| Reference:
|
[4] Cavalheiro, A. C.: Uniqueness of solutions for some degenerate nonlinear elliptic equations.Appl. Math. (Warsaw), 41, 1, 2014, 93-106, Zbl 1324.35039, MR 3241062, 10.4064/am41-1-8 |
| Reference:
|
[5] Cavalheiro, A. C.: Existence and uniqueness of solutions for the Navier problems with degenerate nonlinear elliptic equations.Note Mat., 25, 2, 2015, 1-16, MR 3483422 |
| Reference:
|
[6] Fabes, E., Kenig, C., Serapioni, R.: The local regularity of solutions of degenerate elliptic equations.Comm. Partial Differential Equations, 7, 1982, 77-116, doi:10.1080/03605308208820218. Zbl 0498.35042, MR 0643158, 10.1080/03605308208820218 |
| Reference:
|
[7] 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, Zbl 0859.35062, MR 1402676, 10.4171/RMI/206 |
| Reference:
|
[8] Garcia-Cuerva, J., Francia, J. L. Rubio de: Weighted Norm Inequalities and Related Topics.North-Holland Mathematics Studies, 116, 1985, MR 0807149 |
| Reference:
|
[9] Heinonen, J., Kilpeläinen, T., Martio, O.: Nonlinear Potential Theory of Degenerate Elliptic Equations.1993, Oxford Math. Monographs, Clarendon Press, Zbl 0780.31001, MR 1207810 |
| Reference:
|
[10] Kufner, A.: Weighted Sobolev Spaces.1985, John Wiley & Sons, New York, Zbl 0579.35021, MR 0802206 |
| Reference:
|
[11] Muckenhoupt, B.: Weighted norm inequalities for the Hardy maximal function.Trans. Amer. Math. Soc., 165, 1972, 207-226, Zbl 0236.26016, MR 0293384, 10.1090/S0002-9947-1972-0293384-6 |
| Reference:
|
[12] Torchinsky, A.: Real-Variable Methods in Harmonic Analysis.1986, Academic Press, San Diego, Zbl 0621.42001, MR 0869816 |
| Reference:
|
[13] Turesson, B. O.: Nonlinear Potential Theory and Weighted Sobolev Spaces.1736, 2000, Springer-Verlag, Lecture Notes in Math.. Zbl 0949.31006, MR 1774162, 10.1007/BFb0103912 |
| . |
