论文标题
非本地方程的较高的Hölder规律性不规则内核
Higher Hölder regularity for nonlocal equations with irregular kernel
论文作者
论文摘要
我们研究了一类具有满足温和连续性假设的核的非线性非斜椭圆方程的局部弱解的较高的赫德尔规律性。我们主要结果的一个有趣特征是，在考虑具有连续系数的差异形式的局部椭圆方程的相应结果时，获得的规律性比人们预期的要好。因此，从某种意义上说，遵循近年来观察到的各种这种纯粹的非局部现象的趋势，我们的结果可以被认为是纯粹的非局部类型。我们的方法可以总结如下。首先，我们使用涉及离散分数衍生物的某些测试功能，以获取由局部翻译不变的内核驱动的均匀方程的较高的hölder规律性，而允许内核的全局行为更为笼统。这使我们能够通过近似参数推断出一般情况下的期望规律性。
We study the higher Hölder regularity of local weak solutions to a class of nonlinear nonlocal elliptic equations with kernels that satisfy a mild continuity assumption. An interesting feature of our main result is that the obtained regularity is better than one might expect when considering corresponding results for local elliptic equations in divergence form with continuous coefficients. Therefore, in some sense our result can be considered to be of purely nonlocal type, following the trend of various such purely nonlocal phenomena observed in recent years. Our approach can be summarized as follows. First, we use certain test functions that involve discrete fractional derivatives in order to obtain higher Hölder regularity for homogeneous equations driven by a locally translation invariant kernel, while the global behaviour of the kernel is allowed to be more general. This enables us to deduce the desired regularity in the general case by an approximation argument.
