Abstract
We consider parabolic systems u t − div(a(∇u)) = f in two space dimensions where the elliptic part is derived from a potential and is coercive, but not monotone. With natural assumptions on the data we obtain the existence of a long-time Hölder continuous solution in the sense of Young measures.
Acknowledgements
This research was supported by the DFG, SFB 611 ‘Singuläre Phänomene und Skalierung in mathematischen Modellen’ and the SFB/TR TRR 30 ‘Prozessintegrierte Herstellung funktional gradierter Strukturen auf der Grundlage thermomechanisch gekoppelter Phänomene’.