| Title:
|
Regularity of weak solutions to certain degenerate elliptic equations (English) |
| Author:
|
Cavalheiro, Albo Carlos |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
47 |
| Issue:
|
4 |
| Year:
|
2006 |
| Pages:
|
681-693 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this article we establish the existence of higher order weak derivatives of weak solutions of Dirichlet problem for a class of degenerate elliptic equations. (English) |
| Keyword:
|
degenerate elliptic equations |
| Keyword:
|
weighted Sobolev spaces |
| MSC:
|
35D10 |
| MSC:
|
35J25 |
| MSC:
|
35J70 |
| idZBL:
|
Zbl 1150.35051 |
| idMR:
|
MR2337422 |
| . |
| Date available:
|
2009-05-05T17:00:34Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119628 |
| . |
| Reference:
|
[1] Fabes E., Jerison D., Kenig C.: The Wiener test for degenerate elliptic equations.Ann. Inst. Fourier (Grenoble) 32 3 (1982), 151-182. MR 0688024 |
| Reference:
|
[2] Fabes E., Kenig C., Serapioni R.: The local regularity of solutions of degenerate elliptic equations.Comm. Partial Differential Equations 7 1 (1982), 77-116. Zbl 0498.35042, MR 0643158 |
| Reference:
|
[3] Franchi B., Serapioni R.: Pointwise estimates for a class of strongly degenerate elliptic operators: a geometrical approach.Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 14 4 (1987), 527-568. Zbl 0685.35046, MR 0963489 |
| Reference:
|
[4] Garcia-Cuerva J., Rubio de Francia J.: Weighted Norm Inequalities and Related Topics.North-Holland Mathematics Studies 116, North-Holland, Amsterdam, 1985. MR 0848147 |
| Reference:
|
[5] Gilbarg D., Trudinger N.: Elliptic Partial Differential Equations of Second Order.Springer, Berlin-New York, 1977. Zbl 1042.35002, MR 0473443 |
| Reference:
|
[6] Heinonen J., Kilpeläinen T., Martio O.: Nonlinear Potential Theory of Degenerate Elliptic Equations.Oxford Mathematical Monographs, Oxford University Press, New York, 1993. MR 1207810 |
| Reference:
|
[7] Muckenhoupt B.: Weighted norm inequalities for the Hardy maximal function.Trans. Amer. Math. Soc. 165 (1972), 207-226. Zbl 0236.26016, MR 0293384 |
| Reference:
|
[8] Turesson B.O.: Nonlinear potential theory and weighted Sobolev spaces.Lecture Notes in Math. 1736, Springer, Berlin, 2000. Zbl 0949.31006, MR 1774162 |
| . |
