论文标题
非线性非局部方程的较高的可集成性具有不规则内核
Higher integrability for nonlinear nonlocal equations with irregular kernel
论文作者
论文摘要
我们证明，在贝塞尔电势空间的集成性尺度上，在内核上轻度连续性假设下，沿贝塞尔电势空间的集成性量表$ h^{s，p} $的非线性非局部方程的解决方案较高。通过嵌入，这也可以在Sobolev-slobodeckij空间$ W^{s，p} $中产生规律性。我们的方法是基于贝塞尔电位空间的特征，以某些非局部梯度型操作员和以差异形式使用的局部椭圆方程式中通常使用的扰动方法。
We prove a higher regularity result for weak solutions to nonlinear nonlocal equations along the integrability scale of Bessel potential spaces $H^{s,p}$ under a mild continuity assumption on the kernel. By embedding, this also yields regularity in Sobolev-Slobodeckij spaces $W^{s,p}$. Our approach is based on a characterization of Bessel potential spaces in terms of a certain nonlocal gradient-type operator and a perturbation approach commonly used in the context of local elliptic equations in divergence form.
