论文标题
发散量表：高斯绿色公式和正常痕迹
Divergence-Measure Fields: Gauss-Green Formulas and Normal Traces
论文作者
论文摘要
通常以$ c^{1} $ vector字段和带有$ c^{1} $边界的域表示，用于多维情况的经典高斯绿色公式通常表示。然而，受部分微分方程（PDES）（PDE）和变化的计算（例如非线性双曲线保护法和欧拉 - 拉格朗日方程）的物理解决方案的促进，以下基本问题出现： 高斯绿色公式是否仍然适用于具有不连续性/奇异性（例如差异量磁场）和具有粗糙边界的域的矢量场？ 本文的目的是为这个问题提供答案，并对许多数学家的贡献进行简短的历史回顾，这些数学家跨越了两个多世纪，这使得发现了高斯 - 绿色公式。
The classical Gauss-Green formula for the multidimensional case is generally stated for $C^{1}$ vector fields and domains with $C^{1}$ boundaries. However, motivated by the physical solutions with discontinuity/singularity for Partial Differential Equations (PDEs) and Calculus of Variations, such as nonlinear hyperbolic conservation laws and Euler-Lagrange equations, the following fundamental issue arises: Does the Gauss-Green formula still hold for vector fields with discontinuity/singularity (such as divergence-measure fields) and domains with rough boundaries? The objective of this paper is to provide an answer to this issue and to present a short historical review of the contributions by many mathematicians spanning more than two centuries, which have made the discovery of the Gauss-Green formula possible.
