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Article

Kalita, E.
On the Hölder continuity of solutions of nonlinear parabolic systems. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 35 (1994), issue 4, pp. 675-680
MSC: 35B65, 35D10, 35K40, 35K55 | MR 1321237 | Zbl 0814.35011
Keywords:
non-linear parabolic systems; weak solutions; regularity
Summary:
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.
References:
[1] Kalita E.A.: On sharp exponent of smoothness of solutions to the second order elliptic systems (in Russian). Izvestija Vyshyh Uchebnych Zavedenij. Matematika (1992), 3 10-17. MR 1204810
[2] Koshelev A.I., Chelkak S.I.: Regularity of solutions of quasilinear elliptic systems. Teubner Leipzig (1985). MR 0825485 | Zbl 0581.35003
[3] Koshelev A.I.: Regularity of solutions for some quasilinear parabolic systems. Math. Nachr. 162 (1993), 59-88. MR 1239576 | Zbl 0811.35064
[4] Giaquinta M., Modica G.: 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
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