| Title:
|
Nonlinear degenerate elliptic equations with measure data (English) |
| Author:
|
Li, Fengquan |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
48 |
| Issue:
|
4 |
| Year:
|
2007 |
| Pages:
|
647-658 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we prove existence results for some nonlinear degenerate elliptic equations with data in the space of bounded Radon measures and we improve the results already obtained in Cirmi G.R., {\it On the existence of solutions to non-linear degenerate elliptic equations with measure data\/}, Ricerche Mat. {\bf 42} (1993), no. 2, 315--329. (English) |
| Keyword:
|
nonlinear degenerate elliptic equations |
| Keyword:
|
existence |
| Keyword:
|
measure data |
| MSC:
|
35A35 |
| MSC:
|
35J25 |
| MSC:
|
35J60 |
| MSC:
|
35J70 |
| MSC:
|
35R05 |
| idZBL:
|
Zbl 1197.35107 |
| idMR:
|
MR2375165 |
| . |
| Date available:
|
2009-05-05T17:05:21Z |
| Last updated:
|
2012-05-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119687 |
| . |
| Reference:
|
[1] Boccardo L., Gallouët T.: Nonlinear elliptic and parabolic equations involving measure data.J. Funct. Anal. 87 (1989), 149-169. MR 1025884 |
| Reference:
|
[2] Boccardo L., Gallouët T.: Nonlinear elliptic equations with right hand side measures.Comm. Partial Differential Equations 17 3-4 (1992), 641-655. MR 1163440 |
| Reference:
|
[3] Rakotoson J.M.: Quasilinear elliptic problems with measure as data.Differential Integral Equations 4 (1991), 449-457. MR 1097910 |
| Reference:
|
[4] Rakotoson J.M.: Generalized solutions in a new type of sets for problems with measures as data.Differential Integral Equations 6 1 (1993), 27-36. Zbl 0780.35047, MR 1190163 |
| Reference:
|
[5] Bénilan Ph., Boccardo L., Gallouët T., Gariepy R., Pierre M., Vazquez J.L.: An $L^1$-theory of existence and uniqueness of solutions of non-linear elliptic equations.Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 22 2 (1995), 241-273. MR 1354907 |
| Reference:
|
[6] Dal Maso G., Murat F., Orsina L., Prignet A.: Renormalized solutions of elliptic equations with general measure data.Ann. Scuola Norm. Sup. Pisa. Cl. Sci. (4) 28 4 (1999), 741-808. MR 1760541 |
| Reference:
|
[7] Cirmi G.R.: On the existence of solutions to non-linear degenerate elliptic equations with measure data.Ricerche Mat. 42 2 (1993), 315-329. MR 1283363 |
| Reference:
|
[8] Rakotoson J.M.: Resolution of the critical cases for problems with $L^1$ data.Asymptotic Analysis 6 (1993), 285-293. MR 1201197 |
| Reference:
|
[9] Heinonen J., Kilpeläinen T., Martio O.: Nonlinear Potential Theory of Degenerate Elliptic Equations.Oxford Mathematical Monographs, Clarendon Press, Oxford, 1993. MR 1207810 |
| Reference:
|
[10] Murthy M.K.V., Stampacchia G.: Boundary value problems for some degenerate elliptic operators.Ann. Mat. Pura Appl. 90 (1971), 1-122. Zbl 0226.35037, MR 0249828 |
| Reference:
|
[11] Leray J., Lions J.L.: Quelques résultats de Višik sur les problèmes elliptiques nonlinéaires par les méthodes de Minty et Browder.Bull. Soc. Math. France 93 (1965), 97-107. MR 0194733 |
| Reference:
|
[12] Lions J.L.: Quelques méthodes de résolution des problèmes aux limites nonlinéaires.Dunod, Paris, 1969. |
| Reference:
|
[13] Porretta A.: Some remarks on the regularity of solutions for a class of elliptic equations with measure data.Houston. J. Math. 26 1 (2000), 183-213. Zbl 0974.35032, MR 1814734 |
| Reference:
|
[14] Li F.Q.: Nonlinear degenerate parabolic equations with measure data.Nonlinear Anal. 61 (2005), 1269-1282. Zbl 1073.35133, MR 2131654 |
| . |
