An elliptic variational problem involving level surface area on Riemannian manifolds
An elliptic variational problem involving level surface area on Riemannian manifolds
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涉及黎曼流形上水平表面积的椭圆变分问题
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
Lei Zhang
中科院分区：
文献类型：
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作者：
E. Teixeira;Lei Zhang
研究了任意n维黎曼流形上的一个包含Dirichlet积分和水平曲面面积的变分问题。我们证明了最优正则性结果的极小，并推导出一个跳跃条件沿着水平表面。我们也得到光滑的界面，直到一个小的奇异集的豪斯多夫维数小于或等于n− 8。
We study a variational problem involved with a Dirichlet integral and the area of a level surface on arbitrary n-dimensional Riemannian manifolds. We prove optimal regularity results for minimizers and derive a jumping condition along the level surface. We also obtain smoothness of the interface up to a small singular set of Hausdorff dimension less then or equal to n− 8.