An estimate concerning the difference between minimizer and boundary value in some polyconvex problems

Abstract This paper is concerned with regularity of minimizers of integral functionals with polyconvex potentials. In particular we obtain bounds on the difference | u − u ∗ | ∞ for minimizers u : Ω ⊂ R 3 → R 3 of problem min ∫ Ω f ( x , D v ( x ) ) d x , v ∈ u ∗ + W 0 1 , p ( Ω , R 3 ) .