Regularity theory of the gradient for general nonlinear parabolic systems

Abstract

In this article, we prove partial Hölder regularity of the spatial gradient of weak solutions to a nonlinear parabolic system of second order in divergence form in the case of quadratic growth in the gradient.

Keywords:

• regularity of spatial gradient
• weak solutions
• nonlinear parabolic systems

AMS Subject Classifications::

• 35K55
• 35B65
• 35D30

Acknowledgements

The authors thank the anonymous referee for the accuracy and the depth of remarks and suggestions that contributed to improve this article.