论文标题
抽象插差方程的最大规律性属性
The maximal regularity property of abstract integro-differential equations
论文作者
论文摘要
我们为研究一般Banach函数空间中各种抽象（Integro）微分方程的适当性提供了方便的框架。它使我们能够扩展并补充有关此类方程式最大规律性的已知理论。 更确切地说，通过谐波分析方法，我们确定了大量的Banach空间，这些空间相对于分布傅立叶乘数是不变的。这样的类包括通用矢量值Banach功能空间$φ$和/或BESOV和Triebel-Lizorkin的尺度由$φ$定义。 我们将此结果应用于对抽象二阶差异方程的适合性和最大规律性特性的研究，该方程模拟了在应用数学的不同领域引起的各种类型的椭圆形和抛物线问题。
We provide a convenient framework for the study of the well-posedness of a variety of abstract (integro)differential equations in general Banach function spaces. It allows us to extend and complement the known theory on the maximal regularity of such equations. More precisely, by methods of harmonic analysis, we identify large classes of Banach spaces which are invariant with respect to distributional Fourier multipliers. Such classes include general vector-valued Banach function spaces $Φ$ and/or the scales of Besov and Triebel-Lizorkin spaces defined by $Φ$. We apply this result to the study of the well-posedness and maximal regularity property of abstract second-order integro-differential equation, which models various types of elliptic and parabolic problems arising in different areas of applied mathematics.
