论文标题
凸域中的平面最小梯度问题：不连续的情况
The planar Least Gradient problem in convex domains: the discontinuous case
论文作者
论文摘要
我们研究了平面中的凸多边形集中的两个维度最小梯度问题，即$ω$。当在痕量意义上获得边界数据$ f $时，我们显示了解决方案的存在。这里的主要困难是$ f $的不连续性。此外，由于缺乏$ω$的严格凸度，经典结果不适用。我们声明边界基准$ f $上的可接受性条件，足以建立存在结果。其中之一是bv（\partialΩ）$中的$ f \。解决方案是通过限制过程构建的，该过程使用解决方案来解决已知问题
We study the two dimensional least gradient problem in convex polygonal sets in the plane, $Ω$. We show the existence of solutions when the boundary data $f$ are attained in the trace sense. The main difficulty here is a possible discontinuity of $f$. Moreover, due to the lack of strict convexity of $Ω$, the classical results are not applicable. We state the admissibility conditions on the boundary datum $f$, that are sufficient for establishing an existence result. One of them is that $f\in BV(\partialΩ)$. The solutions are constructed by a limiting process, which uses solutions to known problems
