一个给定平均曲率方程的Dirichlet问题

Pub Date : 2019-08-19 DOI:10.32917/hmj/1607396492

Y. Tsukamoto

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引用次数: 4

摘要

我们研究了一个规定的平均曲率问题，其中我们寻找一个平均曲率向量与给定向量场的法向分量重合的曲面。我们证明了如果指定的向量场在维数尖锐的Sobolev范数中足够小，则该问题在图形最小曲面附近具有解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The Dirichlet problem for a prescribed mean curvature equation

We study a prescribed mean curvature problem where we seek a surface whose mean curvature vector coincides with the normal component of a given vector field. We prove that the problem has a solution near a graphical minimal surface if the prescribed vector field is sufficiently small in a dimensionally sharp Sobolev norm.

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