Local Lipschitz regularity of vector valued local minimizers of variational integrals with densities depending on the modulus of the gradient

Abstract

If u:\mathbb{R}^{n}\supset\Omega\rightarrow\mathbb{R}^{M} locally minimizes the functional \int_{\Omega}h(\left|\nabla u\right|)dx with h such that \frac{h'(t)}{t}\leq h''(t)\leq c(t+t^{2})^{\omega}\frac{h'(t)}{t} for all t\geq0, then u is locally Lipschitz independent of the value of \omega\geq0.