| Title:
|
Existence of a classical solution for linear parabolic systems of nondivergence form (English) |
| Author:
|
Misawa, Masashi |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
45 |
| Issue:
|
3 |
| Year:
|
2004 |
| Pages:
|
475-482 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove the unique existence of a classical solution for a linear parabolic system of nondivergence and nondiagonal form. The key ingredient is to combine the energy estimates with Schauder estimates and to obtain a uniform boundedness of a solution. (English) |
| Keyword:
|
linear parabolic system |
| Keyword:
|
nondivergence |
| Keyword:
|
nondiagonal form |
| Keyword:
|
$L^{\infty }$-estimate |
| Keyword:
|
\newline Schauder estimate |
| MSC:
|
35A05 |
| MSC:
|
35B45 |
| MSC:
|
35D10 |
| MSC:
|
35K40 |
| MSC:
|
35K50 |
| idZBL:
|
Zbl 1098.35073 |
| idMR:
|
MR2103141 |
| . |
| Date available:
|
2009-05-05T16:46:36Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119474 |
| . |
| Reference:
|
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| Reference:
|
[2] Giaquinta M.: Multiple integrals in the calculus of variations and nonlinear elliptic systems.Annals of Mathematics Studies {105}, Princeton Univ. Press, Princeton, NJ, 1983. Zbl 0516.49003, MR 0717034 |
| Reference:
|
[3] Giaquinta M.: Introduction to Regularity Theory for Nonlinear Elliptic Systems.Birkhäuser Verlag, Basel, 1993. Zbl 0786.35001, MR 1239172 |
| Reference:
|
[4] Giaquinta M., Struwe M.: On the regularity of weak solutions of nonlinear parabolic systems.Math. Z. 179 (1982), 437-451. MR 0652852 |
| Reference:
|
[5] Misawa M.: Existence and regularity results for the gradient flow for $p$-harmonic maps.Electron. J. Diff. Equations 1998 (1998), 36 1-17. Zbl 0948.58013, MR 1658020 |
| Reference:
|
[6] Schlag W.: Schauder and $L^p$ estimates for parabolic systems via Campanato spaces.Comm. Partial Differential Equations 21 7-8 (1996), 1141-1175. MR 1399194 |
| Reference:
|
[7] Struwe M.: Some regularity results for quasilinear parabolic systems.Comment. Math. Univ. Carolinae 26 (1985), 129-150. MR 0797297 |
| . |
