Higher Hölder regularity for nonlocal equations with irregular kernel
Higher Hölder regularity for nonlocal equations with irregular kernel
复制标题
具有不规则核的非局部方程的更高 Hölder 正则性
DOI：
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发表时间：
2020
影响因子：
2.1
通讯作者：
Simon Nowak
中科院分区：
文献类型：
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作者：
Simon Nowak
研究了一类满足温和连续性假设的非线性非局部椭圆型方程局部弱解的高Hölder正则性。我们的主要结果的一个有趣的特征是，当考虑具有连续系数的散度形式的局部椭圆方程的相应结果时，所得到的正则性比人们所期望的要好。因此，在某种意义上，我们的结果可以被认为是纯非局部类型，遵循近年来观察到的各种纯非局部现象的趋势。我们的方法可以概括如下。首先，我们使用涉及离散分数阶导数的某些测试函数，以获得由局部平移不变核驱动的齐次方程的更高Hölder规律性，而核的全局行为被允许更一般。这使我们能够在一般情况下通过近似论证推导出所需的规律性。
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.
影响因子：
1.7
作者：
T. Mengesha;A. Schikorra;Sasikarn Yeepo
通讯作者：
T. Mengesha;A. Schikorra;Sasikarn Yeepo