论文标题
与边界一部分施加的Dirichlet条件的最小梯度问题
Least gradient problem with Dirichlet condition imposed on a part of the boundary
论文作者
论文摘要
在边界数据仅在边界的一部分上施加边界数据时，我们提供了最小梯度问题的分析。首先，我们使用凸双重理论在一般环境中对解决方案进行表征。然后，我们讨论解决方案达到其边界价值，解决方案结构及其规律性的方式。
We provide an analysis of the least gradient problem in the case when the boundary datum is only imposed on a part of the boundary. First, we give a characterisation of solutions in a general setting using convex duality theory. Then, we discuss the way in which solutions attain their boundary values, structure of solutions and their regularity.
