Variational integrals on Orlicz-Sobolev spaces (Q1393102)

The existence and the regularity of vector functions \(u:\Omega\subset \mathbb R^n \rightarrow \mathbb R^N \)minimizing variational integrals in the form \(\int_\Omega G(\nabla u) dx\) are studied. The function \(G\) is assumed to be convex and its growth properties are described in terms of an \(N\)-function which is subquadratic at infinity. In particular it is not required that \(G\) grows as a power. Under additional technical assumptions on \(G\), \(C^{1,\alpha}\) regularity of \(u\) is proved, when \(n=2\). When \(n\geq 3\) only partial regularity of \(u\) is obtained.