Non-linear second order parabolic systems in the divergent form are considered. It is proved that under some restrictions on the modulus of ellipticity, all weak solutions are continuous.
@article{118708,
author = {E. A. Kalita},
title = {On the H\"older continuity of solutions of nonlinear parabolic systems},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {35},
year = {1994},
pages = {675-680},
zbl = {0814.35011},
mrnumber = {1321237},
language = {en},
url = {http://dml.mathdoc.fr/item/118708}
}
Kalita, E. A. On the Hölder continuity of solutions of nonlinear parabolic systems. Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) pp. 675-680. http://gdmltest.u-ga.fr/item/118708/
On sharp exponent of smoothness of solutions to the second order elliptic systems (in Russian), Izvestija Vyshyh Uchebnych Zavedenij. Matematika (1992), 3 10-17. (1992) | MR 1204810
Regularity of solutions of quasilinear elliptic systems, Teubner Leipzig (1985). (1985) | MR 0825485 | Zbl 0581.35003
Regularity of solutions for some quasilinear parabolic systems, Math. Nachr. 162 (1993), 59-88. (1993) | MR 1239576 | Zbl 0811.35064
Regularity results for some classes of higher order non linear elliptic systems, J. Reine Angew. Math. 311/312 145-169. | MR 0549962 | Zbl 0409.35015