| Title:
|
An existence and approximation theorem for solutions of degenerate quasilinear elliptic equations (English) |
| Author:
|
Cavalheiro, Albo Carlos |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
59 |
| Issue:
|
1 |
| Year:
|
2018 |
| Pages:
|
65-80 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The main result establishes that a weak solution of degenerate quasilinear elliptic equations can be approximated by a sequence of solutions for non-degenerate quasilinear elliptic equations. (English) |
| Keyword:
|
degenerate quasilinear elliptic equations |
| Keyword:
|
weighted Sobolev spaces |
| MSC:
|
35D30 |
| MSC:
|
35J62 |
| MSC:
|
35J70 |
| idZBL:
|
Zbl 06890397 |
| idMR:
|
MR3783809 |
| DOI:
|
10.14712/1213-7243.2015.232 |
| . |
| Date available:
|
2018-04-17T13:46:20Z |
| Last updated:
|
2020-04-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147179 |
| . |
| Reference:
|
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| Reference:
|
[2] Cavalheiro A. C.: An approximation theorem for solutions of degenerate elliptic equations.Proc. Edinb. Math. Soc. 45 (2002), 363–389; doi: 10.1017/S0013091500000079. 10.1017/S0013091500000079 |
| Reference:
|
[3] Cavalheiro A. C.: Existence of solution for Dirichlet problem of some degenerate quasilinear elliptic equations.J. Adv. Res. Appl. Math. 6 (2014), no. 4, 46–58; doi: 10.5373/jaram.1978.022014. 10.5373/jaram.1978.022014 |
| Reference:
|
[4] Colombo M.: Flows of Non-Smooth Vector Fields and Degenerate Elliptic Equations: With Applications to the Vlasov-Poisson and Semigeostrophic Systems.Publications of the Scuolla Normale Superiore Pisa, 22, Pisa, 2017. |
| Reference:
|
[5] 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. 10.1080/03605308208820218 |
| Reference:
|
[6] Fernandes J. C., Franchi B.: Existence and properties of the Green function for a class of degenerate parabolic equations.Rev. Mat. Iberoamericana 12 (1996), 491–525. 10.4171/RMI/206 |
| Reference:
|
[7] Garcia-Cuerva J., Rubio de Francia J. L.: Weighted Norm Inequalities and Related Topics.North-Holland Mathematics Studies, 116, North Holland Publishing Co., Amsterdam, 1985. |
| Reference:
|
[8] Heinonen J., Kilpeläinen T., Martio O.: Nonlinear Potential Theory of Degenerate Elliptic Equations.Oxford Math. Monographs, The Clarendon Press, Oxford University Press, New York, 1993. |
| Reference:
|
[9] Kufner A.: Weighted Sobolev Spaces.John Wiley & Sons, New York, 1985. Zbl 0862.46017 |
| Reference:
|
[10] Muckenhoupt B.: Weighted norm inequalities for the Hardy maximal function.Trans. Amer. Math. Soc. 165 (1972), 207–226. 10.1090/S0002-9947-1972-0293384-6 |
| Reference:
|
[11] Torchinsky A.: Real-Variable Methods in Harmonic Analysis.Academic Press, San Diego, 1986. Zbl 1097.42002 |
| Reference:
|
[12] Turesson B. O.: Nonlinear Potential Theory and Weighted Sobolev Spaces.Lecture Notes in Math., 1736, Springer, Berlin, 2000. 10.1007/BFb0103912 |
| Reference:
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[13] Xu X.: A local partial regularity theorem for weak solutions of degenerate elliptic equations and its applications to the thermistor problem.Differential Integral Equations 12 (1999), no. 1, 83–100. |
| Reference:
|
[14] Zeidler E.: Nonlinear Functional Analysis and its Applications, II/B.Springer, New York, 1990. |
| . |
