Boundary regularity for conformally invariant variational problems with Neumann data
Boundary regularity for conformally invariant variational problems with Neumann data
复制标题
诺伊曼数据共形不变变分问题的边界正则性
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
A. Schikorra
中科院分区：
文献类型：
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作者：
A. Schikorra
抽象的。我们研究了从二维区域到流形的映射的边界正则性，这些映射对于一般的共形不变变分泛函是临界的，并且在边界处垂直地进入支撑流形。例如，调和映射或H曲面，具有部分自由边界条件。在内部已知的是，著名的工作里维埃，这些地图满足一个系统的反对称潜力，从中可以得出正则性的解决方案。证明了这些映射沿着边界满足一个具有非局部反对称边界势的系统，该边界势包含来自内部势和几何Neumann边界条件的信息.然后，我们继续显示这样的系统的解决方案的边界正则性。
Abstract. We study boundary regularity of maps from two-dimensional domains into manifolds which are critical with respect to a generic conformally invariant variational functional and which, at the boundary, enter perpendicularly into a support manifold. For example, harmonic maps, or H-surfaces, with a partially free boundary condition. In the interior it is known, by the celebrated work of Rivière, that these maps satisfy a system with an antisymmetric potential, from which one can derive regularity of the solution. We show that these maps satisfy along the boundary a system with a nonlocal antisymmetric boundary potential which contains information from the interior potential and the geometric Neumann boundary condition. We then proceed to show boundary regularity for solutions to such systems.