| Title:
|
Weak solution for nonlinear degenerate elliptic problem with Dirichlet-type boundary condition in weighted Sobolev spaces (English) |
| Author:
|
Sabri, Abdelali |
| Author:
|
Jamea, Ahmed |
| Author:
|
Talibi Alaoui, Hamad |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
147 |
| Issue:
|
1 |
| Year:
|
2022 |
| Pages:
|
113-129 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the present paper, we prove the existence and uniqueness of weak solution to a class of nonlinear degenerate elliptic $p$-Laplacian problem with Dirichlet-type boundary condition, the main tool used here is the variational method combined with the theory of weighted Sobolev spaces. (English) |
| Keyword:
|
degenerate elliptic problem |
| Keyword:
|
existence |
| Keyword:
|
uniqueness |
| Keyword:
|
weak solution |
| Keyword:
|
weighted Sobolev space |
| MSC:
|
35A15 |
| MSC:
|
35J60 |
| MSC:
|
35J65 |
| MSC:
|
74G30 |
| idZBL:
|
Zbl 07547244 |
| idMR:
|
MR4387471 |
| DOI:
|
10.21136/MB.2021.0004-20 |
| . |
| Date available:
|
2022-04-17T18:10:44Z |
| Last updated:
|
2022-09-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149593 |
| . |
| Reference:
|
[1] Abassi, A., Hachimi, A. El, Jamea, A.: Entropy solutions to nonlinear Neumann problems with $L^1$-data.Int. J. Math. Stat. 2 (2008), 4-17. Zbl 1137.35033, MR 2348474 |
| Reference:
|
[2] Cavalheiro, A. C.: Weighted Sobolev spaces and degenerate elliptic equations.Bol. Soc. Parana. Mat. (3) 26 (2008), 117-132. Zbl 1185.46024, MR 2505460, 10.5269/bspm.v26i1-2.7415 |
| Reference:
|
[3] Cavalheiro, A. C.: Existence and uniqueness of solutions for some degenerate nonlinear Dirichlet problems.J. Appl. Anal. 19 (2013), 41-54. Zbl 1278.35086, MR 3069764, 10.1515/jaa-2013-0003 |
| Reference:
|
[4] Cavalheiro, A. C.: Existence results for Dirichlet problems with degenerated $p$-Laplacian and $p$-biharmonic operators.Appl. Math. E-Notes 13 (2013), 234-242. Zbl 1291.35053, MR 3159293 |
| Reference:
|
[5] Cavalheiro, A. C.: Existence and uniqueness of solutions for Dirichlet problems with degenerate nonlinear elliptic operators.Differ. Equ. Dyn. Syst. 24 (2016), 305-317. Zbl 1361.35065, MR 3515045, 10.1007/s12591-014-0214-x |
| Reference:
|
[6] Chen, Y., Levine, S., Rao, M.: Variable exponent, linear growth functionals in image restoration.SIAM J. Appl. Math. 66 (2006), 1383-1406. Zbl 1102.49010, MR 2246061, 10.1137/050624522 |
| Reference:
|
[7] Diaz, J. I., Thelin, F. De: On a nonlinear parabolic problem arising in some models related to turbulent flows.SIAM J. Math. Anal. 25 (1994), 1085-1111. Zbl 0808.35066, MR 1278892, 10.1137/S0036141091217731 |
| Reference:
|
[8] Drábek, P.: The least eigenvalues of nonhomogeneous degenerated quasilinear eigenvalue problems.Math. Bohem. 120 (1995), 169-195. Zbl 0839.35049, MR 1357600, 10.21136/MB.1995.126227 |
| Reference:
|
[9] Drábek, P., Kufner, A., Mustonen, V.: Pseudo-monotonicity and degenerated or singular elliptic operators.Bull. Aust. Math. Soc. 58 (1998), 213-221. Zbl 0913.35051, MR 1642031, 10.1017/S0004972700032184 |
| Reference:
|
[10] Hästö, P. A.: The $p(x)$-Laplacian and applications.J. Anal. 15 (2007), 53-62. Zbl 1185.46020, MR 2554092 |
| Reference:
|
[11] Kilpeläinen, J. Heinonen,T., Martio, O.: Nonlinear Potential Theory of Degenerate Elliptic Equations.Oxford Mathematical Monographs. Clarendon Press, Oxford (1993). Zbl 0780.31001, MR 1207810 |
| Reference:
|
[12] Lions, J. L.: Quelques méthodes de résolution des problèmes aux limites non linéaires.Etudes mathematiques. Dunod, Paris (1969), French. Zbl 0189.40603, MR 0259693 |
| Reference:
|
[13] užička, M. R\accent23: Electrorheological Fluids: Modeling and Mathematical Theory.Lectures Notes in Mathematics 1748. Springer, Berlin (2000). Zbl 0962.76001, MR 1810360, 10.1007/BFb0104029 |
| Reference:
|
[14] Turesson, B. O.: Nonlinear Potential Theory and Weighted Sobolev Spaces.Lecture Notes in Mathematics 1736. Springer, Berlin (2000). Zbl 0949.31006, MR 1774162, 10.1007/BFb0103908 |
| . |
