AI 中文总结
研究粗糙区域上散度测度张量场的高斯 - 格林公式，通过引入新配对概念扩展经典理论，调整法向迹定义，建立低正则性集合上的公式，为不规则张量场和区域的分部积分提供统一强大框架。
AI 中文摘要
我们引入了本质有界散度测度张量场与有界变差向量值函数之间的配对概念，将经典理论扩展到张量情形。这自然地导致了即使在可求积集上，对具有测度散度的张量场法向迹定义的调整。结果，我们建立了在低正则性集合（包括有限周长集合）上仍然有效的张量高斯 - 格林公式。这些结果为存在不规则张量场和区域时的分部积分提供了一个统一且强大的框架。
英文摘要
We introduce a notion of pairing between essentially bounded tensor fields with divergence measure and vector-valued functions of bounded variation, extending the classical theory to the tensorial setting. This naturally leads to an adaptation of the definition of normal trace for tensor fields with measure divergence even on a rectifiable set. As a consequence, we establish tensorial Gauss-Green formulas that remain valid on sets with low regularity, including sets of finite perimeter. These results yield a unified and robust framework for integration by parts in the presence of irregular tensor fields and domains.
Comments23 pages
