Boundary regularity of stationary biharmonic maps
Boundary regularity of stationary biharmonic maps
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平稳双调和映射的边界正则性
DOI：
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发表时间：
2011
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通讯作者：
Changyou Wang
中科院分区：
文献类型：
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作者：
Huajun Gong;T. Lamm;Changyou Wang
本文考虑从有界光滑区域Omegasubsetmathbb R^n$（$nge 5$）到无边界紧致光滑黎曼流形Nsubsetmathbb R^l$的平稳双调和映射u$的Dirichlet问题。对于任意光滑边界数据，证明了如果u满足一定的边界单调性不等式，则存在一个闭子集Sigmassubset1）A =0，arOmegasetminusSigma，N）$。
We consider the Dirichlet problem for stationary biharmonic maps $u$ from a bounded, smooth domain $Omegasubsetmathbb R^n$ ($nge 5$) to a compact, smooth Riemannian manifold $Nsubsetmathbb R^l$ 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 $Sigmasubsetar{Omega}$, with $H^{n-4}(Sigma)=0$, such that $uin C^infty(arOmegasetminusSigma, N)$.