A remark on the regularity of vector-valued mappings depending on two variables which minimize splitting-type variational integrals

We combine the maximum principle for vector-valued mappings established by D'Ottavio, Leonetti and Musciano [7] with regularity results from [5] and prove the Hölder continuity of the first derivatives for local minimizers u: Ω → ℝN of splitting-type variational integrals provided Ω is a domain in ℝ2.