Boundary regularity for polyharmonic maps in the critical dimension

Abstract

We consider the Dirichlet problem for intrinsic and extrinsic k-polyharmonic maps from a bounded, smooth domain  � R 2k to a compact, smooth Riemannian manifold N � R l without boundary. For any smooth boundary data, we show that any k-polyharmonic map u 2 W k;2 .; N / is smooth near the boundary @.