| Title:
|
Hölder regularity for nonhomogeneous elliptic systems with nonlinearity greater than two (English) |
| Author:
|
Idone, Giovanna |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
54 |
| Issue:
|
4 |
| Year:
|
2004 |
| Pages:
|
817-841 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Regularity results for elliptic systems of second order quasilinear PDEs with nonlinear growth of order $q>2$ are proved, extending results of [7] and [10]. In particular Hölder regularity of the solutions is obtained if the dimension $n$ is less than or equal to $q + 2$. (English) |
| Keyword:
|
nonlinear elliptic systems |
| Keyword:
|
regularity up to the boundary |
| MSC:
|
35B65 |
| MSC:
|
35J55 |
| MSC:
|
35J65 |
| idZBL:
|
Zbl 1080.35031 |
| idMR:
|
MR2099997 |
| . |
| Date available:
|
2009-09-24T11:18:01Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127933 |
| . |
| Reference:
|
[1] S. Campanato: Equazioni ellittiche del secondo ordine e spazi $L^{2, \lambda }$.Ann. Mat. Pura e Appl. 69 (1965), 321–381. MR 0192168, 10.1007/BF02414377 |
| Reference:
|
[2] S. Campanato: Sistemi ellittici in forma di divergenza. Regolarità all’interno.Quaderni S.N.S. di Pisa, 1980. MR 0668196 |
| Reference:
|
[3] S. Campanato: Elliptic systems with nonlinearity $q$ greater or equal to two. Regularity of the solution of the Dirichlet Problem.Ann. Mat. Pura e Appl. 147 (1987), 117–150. Zbl 0635.35038, MR 0916705, 10.1007/BF01762414 |
| Reference:
|
[4] S. Campanato: A maximum principle for nonlinear elliptic systems. Boundary fundamental estimates.Advances in Math. 66 (1987), 291–317. Zbl 0644.35042, MR 0915857, 10.1016/0001-8708(87)90037-5 |
| Reference:
|
[5] S. Campanato: A maximum principle for nonlinear elliptic systems.Atti Convegno commem. di M. Picone e L. Tonelli vol. , Acc. Lincei, Roma, 1985, pp. 173–182. |
| Reference:
|
[6] E. De Giorgi: Un esempio di estremali discontinue per un problema variazionale di tipo ellittico.Boll. Un. Mat. Ital. 1 (1968), 135–137. MR 0227827 |
| Reference:
|
[7] L. Fattorusso, G. Idone: Hölder regularity for nonlinear nonhomogeneous elliptic systems.Le Matematiche 50 (1995), 285–306. MR 1414636 |
| Reference:
|
[8] J. Frehse: On the boundedness of weak solutions of higher order nonlinear elliptic partial differential equations.Boll. Un. Mat. Ital. 4 (1970), 607–627. Zbl 0203.41303, MR 0274938 |
| Reference:
|
[9] J. Serrin: Local behaviour of solutions of quasilinear equations.Acta Math. 111 (1964), 247–302. MR 0170096, 10.1007/BF02391014 |
| Reference:
|
[10] K. Widman: Hölder continuity of solutions of elliptic systems.Manuscripta Math. 5 (1971), 299–308. Zbl 0223.35044, MR 0296484, 10.1007/BF01367766 |
| . |
