Interpolation inequalities for weak solutions of nonlinear parabolic systems

The authors investigate differentiability of the solutions of nonlinear parabolic systems of order 2 m in divergence form of the following type (Equation presented). The achieved results are inspired by the paper of Marino and Maugeri 2008, and the methods there applied. This note can be viewed as a continuation of the study of regularity properties for solutions of systems started in Ragusa 2002, continued in Ragusa 2003 and Floridia and Ragusa 2012 and also as a generalization of the paper by Capanato and Cannarsa 1981, where regularity properties of the solutions of nonlinear elliptic systems with quadratic growth are reached. © 2011 Floridia and Ragusa; licensee Springer.