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

If \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}$u : {\mathbb R}^{n}\supset \Omega \rightarrow {\mathbb R}^{M} $\end{document} locally minimizes the functional ∫ Ω h (|∇ u |) dx with h such that ${{h^{\prime }(t)}\over{t}} \le h^{\prime \prime }(t) \le c\, (1 + t^2)^\omega {{h^{\prime }(t)}\over{t}} $ for all t ⩾ 0, then u is locally Lipschitz independent of the value of ω ⩾ 0. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim