论文标题
平滑域的分数KORN型不平等和非线性非局部方程系统的规律性估计值
A Fractional Korn-type inequality for smooth domains and a regularity estimate for nonlinear nonlocal systems of equations
论文作者
论文摘要
在本文中，我们证明了古典科恩第一个不平等的分数类似物。不等式使得有可能显示矢量场函数空间的等效性，其特征在于gagliardo型静态具有“投影差”与相应的分数Sobolev空间的等效性。作为应用程序，我们将使用它来获得非局部方程的非线性系统的caccioppoli型不平等，这反过来又是应用已知结果的关键成分，以证明非局部方程非线性系统弱溶液的较高分数可不同性结果。我们证明的规律性结果将证明，标量非局部方程的众所周知的自我改善特性也将用于非局部方程的强耦合系统。
In this paper we prove a fractional analogue of the classical Korn's first inequality. The inequality makes it possible to show the equivalence of a function space of vector field characterized by a Gagliardo-type seminorm with 'projected difference' with that of a corresponding fractional Sobolev space. As an application, we will use it to obtain a Caccioppoli-type inequality for a nonlinear system of nonlocal equations, which in turn is a key ingredient in applying known results to prove a higher fractional differentiability result for weak solutions of the nonlinear system of nonlocal equations. The regularity result we prove will demonstrate that a well-known self-improving property of scalar nonlocal equations will hold for strongly coupled systems of nonlocal equations as well.
