| Title:
|
An example of a nonlinear second order elliptic system in three dimension (English) |
| Author:
|
Daněček, Josef |
| Author:
|
Nikodým, Marek |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
45 |
| Issue:
|
3 |
| Year:
|
2004 |
| Pages:
|
431-442 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We provide an explicit example of a nonlinear second order elliptic system of two equations in three dimension to compare two $C^{0,\gamma}$-regularity theories. We show that, for certain range of parameters, the theory developed in {\it Dan\v{e}\v{c}ek, Nonlinear Differential Equations Appl.\/} {\bf 9} (2002), gives a stronger result than the theory introduced in {\it Koshelev, Lecture Notes in Mathematics,} {\bf 1614}, 1995. In addition, there is a range of parameters where the first theory gives H"{o}lder continuity of solution for all $\gamma<1$, while the {\it Koshelev} theory is not applicable at all. (English) |
| Keyword:
|
nonlinear elliptic systems |
| Keyword:
|
regularity |
| Keyword:
|
Campanato-Morrey spaces |
| MSC:
|
35B65 |
| MSC:
|
35D10 |
| MSC:
|
35J45 |
| MSC:
|
35J60 |
| idZBL:
|
Zbl 1105.35035 |
| idMR:
|
MR2103138 |
| . |
| Date available:
|
2009-05-05T16:46:20Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119471 |
| . |
| Reference:
|
[BV] Balanda L., Viszus E.: On Liouville theorem and the regularity of weak solutions to some nonlinear elliptic systems of higher order.Comment. Math. Univ. Carolinae 32.4 (1991), 615-625. Zbl 0773.35017, MR 1159808 |
| Reference:
|
[C1] Campanato S.: Sistemi ellittici in forma divergenza. Regolarita all'interno.Quaderni Scuola Norm. Sup. Pisa Pisa (1980). Zbl 0453.35026, MR 0668196 |
| Reference:
|
[C2] Campanato S.: A maximum principle for non-linear elliptic systems: Boundary fundamental estimates.Adv. in Math. 48 (1983), 16-43. |
| Reference:
|
[D1] Daněček J.: On the interior regularity of weak solutions to nonlinear elliptic systems of second order.Z. Anal. Anwendungen 9.6 (1990), 535-544. MR 1119297 |
| Reference:
|
[D2] Daněček J.: The interior $BMO$-regularity for a weak solution of a nonlinear second order elliptic systems.NoDEA Nonlinear Differential Equations Appl. 9 (2002), 385-396. MR 1941264 |
| Reference:
|
[DJS] Daněček J., John O., Stará J.: The interior $C^{1,\gamma}$-regularity for a weak solution of nonlinear second order elliptic systems.Math. Nachr., to appear. MR 2100046 |
| Reference:
|
[Gia] Giaquinta M.: Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems.Annals of Mathematics Studies 105 Princeton University Press Princeton, NJ (1983). Zbl 0516.49003, MR 0717034 |
| Reference:
|
[Ko] Koshelev A.I.: Regularity Problem for Quasilinear Elliptic and Parabolic System.Lecture Notes in Mathematics 1614 Springer Heidelberg (1995). MR 1442954 |
| Reference:
|
[KJF] Kufner A., John O., Fučík S.: Function Spaces.Academia Prague (1977). MR 0482102 |
| Reference:
|
[Ne] Nečas J.: Introduction to the Theory of Nonlinear Elliptic Equations.Teubner-Texte zur Mathematik Band 52 Leipzig (1983). MR 0731261 |
| Reference:
|
[Nik] Nikodým M.: Thesis, FSI VUT Brno, 2003, 25 pp. (in Czech).. |
| . |
