Elliptic Variational Problems with Nonstandard Growth

For a bounded Lipschitz domain a minimization problem is considered over functions of the Orlicz-Sobolev space generated by an N-function A (with Δ₂-property) that have prescribed trace u₀. Regularity results are established. In the vector case N > 1, partial C1,α-regularity is proved without any additional structural conditions. The results are easily extended to the case of locally minimizing mappings. In the scalar case, the results obtained cover the case of (double) obstacles. Under an additional assumption, the regularity results can be improved (cf. Theorem 3 below which admits the anisotropic two-dimensional vector case).