Zeros for the Gradients of WeaklyA-Harmonic Tensors

The Caccioppoli inequality of weaklyA-harmonic tensors has been proved, which can be used to consider the weak reverse Hölder inequality, regularity property, and zeros of weaklyA-harmonic tensors.

A Caccioppoli inequality and partial regularity in the calculus of variations

SynopsisA new proof is given of the partial regularity of minimisers under the principal assumptions of uniform strict quasiconvexity and polynomial growth. The proof is based on a Caccioppoli inequality and an “indirect” blow-up argument; this avoids the technical complications of a “direct” argument.