| Title:
|
The Neumann problem for some degenerate elliptic equations (English) |
| Author:
|
Cavalheiro, Albo Carlos |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
51 |
| Issue:
|
6 |
| Year:
|
2006 |
| Pages:
|
619-628 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the paper we study the equation $Lu=f$, where $L$ is a degenerate elliptic operator, with Neumann boundary condition in a bounded open set ${\Omega }$. We prove existence and uniqueness of solutions in the space $H(\Omega )$ for the Neumann problem. (English) |
| Keyword:
|
Neumann problem |
| Keyword:
|
degenerate elliptic equations |
| MSC:
|
35J25 |
| MSC:
|
35J70 |
| idZBL:
|
Zbl 1164.35362 |
| idMR:
|
MR2291786 |
| DOI:
|
10.1007/s10492-006-0025-7 |
| . |
| Date available:
|
2009-09-22T18:27:50Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134657 |
| . |
| Reference:
|
[1] S. Chanillo, R. L. Wheeden: Harnack’s inequalities and mean-value inequalities for solutions of degenerate elliptic equations.Commun. PDE 11 (1986), 1111–1134. MR 0847996, 10.1080/03605308608820458 |
| Reference:
|
[2] S. Chanillo, R. L. Wheeden: Existence and estimates for Green’s function for degenerate elliptic equations.Ann. Sc. Norm. Super. Pisa IV ser. 15, Fasc. II (1988), 309–340. MR 1007400 |
| Reference:
|
[3] B. Franchi, R. Serapioni: Pointwise estimates for a class of strongly degenerate elliptic operators: A geometrical approch.Ann. Sc. Norm. Sup. Pisa C1 ser. 14 (1987), 527–568. MR 0963489 |
| Reference:
|
[4] B. Muckenhoupt: Weighted norm inequalities for the Hardy maximal function.Trans. Am. Math. Soc. 165 (1972), 207–226. Zbl 0236.26016, MR 0293384, 10.1090/S0002-9947-1972-0293384-6 |
| Reference:
|
[5] A. Torchinsky: Real-Variable Methods in Harmonic Analysis.Academic Press, Orlando, 1986. Zbl 0621.42001, MR 0869816 |
| Reference:
|
[6] A. Kufner, O. John, and S. Fučík: Function Spaces.Noordhoff International Publishing, Leyden, 1977. MR 0482102 |
| Reference:
|
[7] A. Kufner: Weighted Sobolev Spaces.John Wiley & Sons, New York, 1985. Zbl 0579.35021, MR 0802206 |
| Reference:
|
[8] J. Heinonen, T. Kilpeläinen, and O. Martio: Nonlinear Potential Theory of Degenerate Elliptic Equations. Oxford Math. Monographs.Clarendon Press, Oxford, 1993. MR 1207810 |
| Reference:
|
[9] J. Garcia-Cuerva, J. L. Rubio de Francia: Weighted Norm Inequalities and Related Topics. North-Holland Mathematics Studies 116.North Holland, Amsterdam-New York-Oxford, 1985. MR 0807149 |
| Reference:
|
[10] B. O. Turesson: Nonlinear Potential Theory and Weighted Sobolev Spaces. Lectures Notes in Mathematics Vol. 1736.Springer-Verlag, Berlin, 2000. MR 1774162 |
| Reference:
|
[11] V. Chiadò Piat, F. Serra Cassano: Relaxation of degenerate variational integrals.Nonlinear Anal., Theory Methods Appl. 22 (1994), 409–424. MR 1266369, 10.1016/0362-546X(94)90165-1 |
| . |
