Boundary regularity of stationary biharmonic maps

Details Boundary regularity of stationary biharmonic maps Boundary regularity of stationary biharmonic maps

2011-05-02

arxiv.org/abs/1105.0384v2

Mathematics

Analysis of PDEs

23 pages

Scientific paper

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 $u\in C^\infty(\bar\Omega\setminus\Sigma, N)$.

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