Regularity for a class of integral functionals

This paper deals with regularity properties for variational integrals with the splitting structure of the form J(u,Omega)=integral Omega & sum;i=1n+1fi(x,Dui)+gi(x,(adjnDu)i)dx,$$\begin{equation*} \hspace*{59pt}{\cal J} (u,\Omega) = \int _{\Omega } \sum _{i=1}<^>{n+1} {\left\lbrace f<^>{i}(x,Du<^>{i})+ g<^>{i}(x,({\rm adj} _{n}Du)<^>{i}) \right\rbrace} dx, \end{equation*}$$where u=(u1,u2,& mldr;,un+1):Omega subset of Rn -> Rn+1$u=(u<^>1,u<^>2, \ldots, u<^>{n+1}):\Omega \subset \mathbb {R}<^>n \rightarrow \mathbb {R}<^>{n+1}$, adjnDu is an element of Rn+1${\rm adj}_n Du \in \mathbb {R}<^>{n+1}$ is the adjugate matrix of order n$n$, and fi:Omega xRn -> R$f<^>i:\Omega \times \mathbb {R}<^>{n} \rightarrow \mathbb {R}$, gi:Omega xR -> R$g<^>i:\Omega \times \mathbb {R} \rightarrow \mathbb {R}$, i=1,2,& mldr;,n+1$i=1,2, \ldots, n+1$, are Carath & eacute;odory functions satisfying suitable structural conditions. Local integrability, local boundedness, and local H & ouml;lder continuity for local minimizers are derived.