$\mathcal{A}$-自由测度的绝对连续部分的非刚性
偏微分方程分析
2025-03-26 v3
摘要
我们推广了Alberti的一个结果，表明如果一阶线性微分算子属于某一类，那么任何函数都是满足的测度的绝对连续部分。当是标量值时，我们给出了上述性质成立的充要条件，并证明了奇异部分的维数估计。最后，我们证明了上述类中的算子满足Lusin型性质。
引用
@article{arxiv.2312.06026,
title = {Non-rigidity of the absolutely continuous part of $\mathcal{A}$-free measures},
author = {Luigi De Masi and Carlo Gasparetto},
journal= {arXiv preprint arXiv:2312.06026},
year = {2025}
}
备注
Several examples were added, including the case of exterior derivatives; in that case, it is proved that the exterior derivative operator is balanceable. Other minor corrections from the previous version were included