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扩展分歧测量场,高斯-绿公式和考希流量
Gui-Qiang G Chen1, Christopher Irving2, Monica Torres3
1Mathematical Institute, University of Oxford, Oxford, OX2 6GG UK.
Archive for rational mechanics and analysis
|November 28, 2025
概括
我们为扩展的分歧测量场开发了高斯-格林公式,证明了正常的痕迹在边界上得到支持. 这扩展了连续物理中的平衡定律,将考西定理推广为更广泛的应用.
科学领域:
- 数学分析的数学分析
- 连续体物理 连续体物理
- 矢量计算 矢量计算 矢量计算 矢量计算
背景情况:
- 经典的高斯-格林公式适用于光滑的向量场.
- 扩展的差异测量领域需要一般化表述.
- 连续物理平衡规律传统上假定连续场.
研究的目的:
- 为扩展的差异测量领域建立高斯-格林公式.
- 在连续物理中概括平衡定律.
- 为物理平衡规律提供严格的数学基础.
主要方法:
- 使用矢量值测量和分布差的理论.
- 证明开放集及其边界的正常轨迹的属性.
- 制定衡量值的正常轨迹及其极限的框架.
主要成果:
- 扩展分歧测量场的正常痕迹是在边界上支持的测量.
- 通过近似集的极限推导出正常轨迹的表示.
- 平衡法被扩展到一个一般的框架,使用生产和考奇流的测量.
结论:
- 该研究概括了考契定理,并扩展了以前的考契流量公式.
- 形成PDEs和物理平衡规律的分歧的解决方案之间建立了等价性.
- 这项工作为连续物理提供了一个强大的公理基础.
关键词:
26B05 其他 26B05 其他26B12 26B12 26B12 26B12 26B12 26B12 26B12 26B12 26B12 26B12 26B12 26B12 26B12 26B12 26B12 26B12 2626B20 26B20 26B20 26B20 26B20 26B20 26B20 26B20 26B20 26B20 26B20 26B20 26B20 26B20 26B20 26B20 26B2026B30 其他 26B30 其他 26B3026B4040 其他 其他 其他28A0505 其他 其他28A2525 其他 其他35D3030 35D3030 35D3030 35D30 30D30 35D30 35D30 35D30 35D30 35D30 35D30 35D30 35D3035L6565 这是一个很好的方法.35L6767 这是一个很好的例子.初级: 28C0505 其他二级: 28A7575 年级
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