Stability and Continuity of Functions of Least Gradient
Stability and Continuity of Functions of Least Gradient
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最小梯度函数的稳定性和连续性
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
N. Shanmugalingam
中科院分区：
文献类型：
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作者：
H. Hakkarainen;R. Korte;P. Lahti;N. Shanmugalingam
本文证明了在度量测度空间上，最小梯度函数以及面积泛函（在测度为零的集合上修改后）的局部极小元在其跳集外处处连续.作为一种工具，我们发展了最小梯度函数序列的一些稳定性性质。我们还应用这些工具来证明一个最大值原理的最小梯度的功能，出现作为解决方案的狄利克雷问题。
Abstract In this note we prove that on metric measure spaces, functions of least gradient, as well as local minimizers of the area functional (after modification on a set of measure zero) are continuous everywhere outside their jump sets. As a tool, we develop some stability properties of sequences of least gradient functions. We also apply these tools to prove a maximum principle for functions of least gradient that arise as solutions to a Dirichlet problem.