| Title:
|
On the Hölder continuity of weak solutions to nonlinear parabolic systems in two space dimensions (English) |
| Author:
|
Naumann, J. |
| Author:
|
Wolf, J. |
| Author:
|
Wolff, M. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
39 |
| Issue:
|
2 |
| Year:
|
1998 |
| Pages:
|
237-255 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove the interior Hölder continuity of weak solutions to parabolic systems $$ \frac{\partial u^j}{\partial t}-D_\alpha a_j^\alpha(x,t,u,\nabla u)=0 \text{ in } Q \quad (j=1,\ldots,N) $$ ($Q=\Omega\times(0,T),\Omega\subset\Bbb R^2$), where the coefficients $a_j^\alpha(x,t,u,\xi)$ are measurable in $x$, Hölder continuous in $t$ and Lipschitz continuous in $u$ and $\xi$. (English) |
| Keyword:
|
nonlinear parabolic systems |
| Keyword:
|
Hölder continuity |
| Keyword:
|
Fourier transform |
| MSC:
|
35B65 |
| MSC:
|
35D10 |
| MSC:
|
35K40 |
| MSC:
|
35K55 |
| idZBL:
|
Zbl 0940.35046 |
| idMR:
|
MR1651938 |
| . |
| Date available:
|
2009-01-08T18:40:23Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119003 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[4] Da Prato G.: Spazi ${\Cal L}^{(p,\theta)}(Ømega,\delta)$ e loro proprietà.Ann. Mat. Pura Appl. (4) 69 (1965), 383-392. Zbl 0145.16207, MR 0192330 |
| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
|
[8] Koshelev A.: Regularity of solutions for some quasilinear parabolic systems.Math. Nachr. 162 (1993), 59-88. Zbl 0811.35064, MR 1239576 |
| Reference:
|
[9] Ladyzenskaja O.A., Solonnikov V.A., Ural'ceva N.N.: Linear and quasilinear equations of parabolic type.Transl. Math. Monographs 28, Amer. Math. Soc., Providence, R.I., 1968. MR 0241822 |
| Reference:
|
[10] Naumann J., Wolf J.: Interior differentiability of weak solutions to parabolic systems with quadratic growth nonlinearities.to appear. Zbl 0894.35050, MR 1066428 |
| Reference:
|
[11] Nečas J., Šverák V.: On regularity of nonlinear parabolic systems.Ann. Scuola Norm. Sup. Pisa (4) 18 (1991), 1-11. MR 1118218 |
| . |
