Boundary regularity of stationary biharmonic maps

Abstract

We consider the Dirichlet problem for stationary biharmonic maps $u$ from a bounded, smooth domain $\Omega \subset {\mathbb{R}}^n$ ($n\ge 5$) to a compact, smooth Riemannian manifold $N\subset {\mathbb{R}}^l$ without boundary. For any smooth boundary data, we show that if, in addition, $u$ satisfies a certain boundary monotonicity inequality, then there exists a closed subset $\Sigma \subset \bar{\Omega }$, with $H^{n-4}(\Sigma )=0$, such that $u\in C^{\infty }(\bar{\Omega }\setminus \Sigma ,N)$.

23 pages

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