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arXiv · 1105.0384

Boundary regularity of stationary biharmonic maps

Huajun Gong·Tobias Lamm·Changyou Wang
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Abstract

We consider the Dirichlet problem for stationary biharmonic maps $u$ from a bounded, smooth domain $Ω\subset\mathbb R^n$ ($n\ge 5$) 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 $Σ\subset\barΩ$, with $H^{n-4}(Σ)=0$, such that $u\in C^\infty(\barΩ\setminusΣ, N)$.

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Huajun Gong, Tobias Lamm, Changyou Wang. 2011-05-03. Boundary regularity of stationary biharmonic maps. https://arxiv.org/abs/1105.0384

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