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We propose two new direct methods for proving partial regularity of solutions of nonlinear elliptic or parabolic systems. The methods are based on two similar interpolation inequalities for solutions of linear systems with constant coefficient. The first results from an interpolation inequality of L p norms in combination with an L p estimate with low exponent p > 1 . For the second, we provide a functional-analytic proof, that also sheds light upon the A-harmonic approximation lemma of Duzaar and Steffen. Both methods use a Caccioppoli inequality and avoid higher integrability. We illustrate the methods in detail for the case of a quasilinear elliptic system. [ABSTRACT FROM AUTHOR]

We present polynomials for the eigenprojections or Frobenius covariants of a matrix A ∈ Cn×n. They allow for a computation of a function of A by a generalization of the Sylvester formula. [ABSTRACT FROM AUTHOR]

We prove partial regularity for vector-valued minimizers u of the variational integral ∫ [ f ( x , u , D u ) + g ( x , u ) ] d x , where f is strictly quasiconvex, of polynomial growth and continuous, but where g is only a bounded Carathéodory function. We present an elementary proof for the special case of strict convexity and quadratic growth of f ( x , u , ·). [ABSTRACT FROM AUTHOR]