论文标题
一类非本地方程的梯度规律性和一阶潜在估计值
Gradient regularity and first-order potential estimates for a class of nonlocal equations
论文作者
论文摘要
我们考虑了大于一个具有测量数据的阶数的非局部方程，并且证明了Sobolev和Hölder空间中的梯度规律性以及梯度的渐变范围在Riesz电位方面，导致良好的规律性在许多常用的功能空间中导致了良好的规律性。积分运算符的内核涉及变量中的Hölder依赖性，并且不认为是翻译不变的。
We consider nonlocal equations of order larger than one with measure data and prove gradient regularity in Sobolev and Hölder spaces as well as pointwise bounds of the gradient in terms of Riesz potentials, leading to fine regularity results in many commonly used function spaces. The kernel of the integral operators involves a Hölder dependence in the variables and is not assumed to be translation invariant.
