发表机构
University of Padua; University of Warwick; Bocconi University（帕多瓦大学; 华威大学; 博科尼大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明了受偏微分方程约束的测度在σ-有限H^m测度集合上的质量估计，并据此推导出满足原子条件(AC1)的积分项下具有有界各向异性一阶变分的varifolds的Michael-Simon不等式。
AI 中文摘要
我们证明了在满足适当秩条件下，对具有σ-有限${\mathcal H}^m$测度的集合上受偏微分方程约束的测度，建立了质量估计。作为应用，我们推导出对于具有关于满足自然原子条件(AC1)的积分项的有界各向异性一阶变分的varifolds，成立Michael-Simon不等式。
英文摘要
We prove mass estimates for PDE-constrained measures on sets of $σ$-finite ${\mathcal H}^m$-measure, assuming an appropriate rank condition. As an application, we derive a Michael--Simon inequality for varifolds with bounded anisotropic first variation with respect to an integrand that satisfies the natural atomic condition (AC1).
Comments11 pages; comments are welcome!
