论文标题
公制空间中艾科纳尔方程解决方案的等效性
Equivalence of solutions of eikonal equation in metric spaces
论文作者
论文摘要
在本文中，我们证明了一些已知的溶液概念与二基核方程的一些已知概念与汉密尔顿 - 雅各比方程的更通用的类似物之间的等效性在完整且完整地连接的度量标准空间中。考虑的概念是基于曲线的粘度解决方案，基于坡度的粘度解决方案和Monge解决方案。通过使用诱导的固有（路径）度量，我们将度量空间减少到长度空间，并显示这些解决方案与相关的Dirichlet边界问题的等效性。在不利用边界数据的情况下，我们还本地化了我们的参数，并直接证明了解决方案定义的等效性。还讨论了与欧几里得半cove性有关的解决方案的规律性。
In this paper we prove the equivalence between some known notions of solutions to the eikonal equation and more general analogs of the Hamilton-Jacobi equations in complete and rectifiably connected metric spaces. The notions considered are that of curve-based viscosity solutions, slope-based viscosity solutions, and Monge solutions. By using the induced intrinsic (path) metric, we reduce the metric space to a length space and show the equivalence of these solutions to the associated Dirichlet boundary problem. Without utilizing the boundary data, we also localize our argument and directly prove the equivalence for the definitions of solutions. Regularity of solutions related to the Euclidean semi-concavity is discussed as well.
