Hölder continuous Young measure solutions to coercive non-monotone parabolic systems in two space dimensions

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.

Keywords:

• nonlinear parabolic systems
• Hölder continuity
• Young measure solutions
• convergence of finite elements

AMS Subject Classifications::

• 35K55
• 35K50

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’.