Geodesic
On the Hölder continuity of weak solutions to nonlinear parabolic systems in two space dimensions
Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) no. 2, pp. 237-255 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $\xi$.
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 $\xi$.
Classification : 35B65, 35D10, 35K40, 35K55
Keywords: nonlinear parabolic systems; Hölder continuity; Fourier transform 
@article{CMUC_1998_39_2_a2,
     author = {Naumann, J. and Wolf, J. and Wolff, M.},
     title = {On the {H\"older} continuity of weak solutions to nonlinear parabolic systems in two space dimensions},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {237--255},
     year = {1998},
     volume = {39},
     number = {2},
     mrnumber = {1651938},
     zbl = {0940.35046},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1998_39_2_a2/}
}
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Naumann, J.; Wolf, J.; Wolff, M. On the Hölder continuity of weak solutions to nonlinear parabolic systems in two space dimensions. Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) no. 2, pp. 237-255. http://geodesic.mathdoc.fr/item/CMUC_1998_39_2_a2/