Abstract

We establish a Riesz potential criterion for Lebesgue continuity points of functions of bounded $\mathbb{A}$-variation, where $\mathbb{A}$ is a $\mathbb{C}$-elliptic differential operator of arbitrary order. This result generalizes a potential criterion that is known for full gradients to the case where full gradient estimates are not available by virtue of Ornstein’s non-inequality.

中文翻译：

---

R-椭圆算子的Riesz势连续点

摘要

我们为有界$ \ mathbb {A} $-变异的函数的Lebesgue连续性点建立了一个Riesz潜在准则，其中$ \ mathbb {A} $是任意阶的\\ mathbb {C} $-椭圆微分算子。该结果概括了对于完全梯度已知的潜在标准，以至于由于Ornstein的非等式而无法获得完全梯度估计的情况。