Derivation of a boundary monotonicity inequality for variationally biharmonic maps

We derive a boundary monotonicity formula for a class of biharmonic maps with Dirichlet boundary conditions. A monotonicity formula is crucial in the theory of partial regularity in super-critical dimensions. As a consequence of such a boundary monotonicity formula, one is able to show partial regularity for variationally biharmonic maps and full boundary regularity for minimizing biharmonic maps.