论文标题
加权非自主$ l^q（l^p）$对复杂系统的最大规律性
Weighted non-autonomous $L^q(L^p)$ maximal regularity for complex systems
论文作者
论文摘要
我们在时空和时间的混合规律性条件下显示了加权的非自主$ l^q（l^p）$最大规律性的二阶系统家庭的最大规律性。更确切地说，我们将$ p，q \ in（1，\ infty）$ in（1，\ infty）$，我们考虑$ c^{β+ \ \ varepsilon} $中的系数功能，并在$ c^{α+ \ varepsilon} $中的值，受parabolic关系$2β+α= 1 $。如果$ p <\ frac {d}α$，我们同样可以处理空间$ h^{α+ \ varepsilon，\ frac {d}α} $正常性。该结果的起点是具有统一常数的薄弱$（P，Q）$ - 解决方案理论。更多的关键要素是换向因素的参数，它使我们能够在加权空间中建立更高的先验空间规律性，操作员可价值的伪差分运算符，以及由于Akeristapace和Terreni而引起的表示公式。此外，我们显示了由复杂椭圆系统生成的半群和平方根的$ p $ bounds，该系数的规律性最小，该系数的规律性假设最少。
We show weighted non-autonomous $L^q(L^p)$ maximal regularity for families of complex second-order systems in divergence form under a mixed regularity condition in space and time. To be more precise, we let $p,q \in (1,\infty)$ and we consider coefficient functions in $C^{β+ \varepsilon}$ with values in $C^{α+ \varepsilon}$ subject to the parabolic relation $2β+ α= 1$. If $p < \frac{d}α$, we can likewise deal with spatial $H^{α+ \varepsilon, \frac{d}α}$ regularity. The starting point for this result is a weak $(p,q)$-solution theory with uniform constants. Further key ingredients are a commutator argument that allows us to establish higher a priori spatial regularity, operator-valued pseudo differential operators in weighted spaces, and a representation formula due to Acquistapace and Terreni. Furthermore, we show $p$-bounds for semigroups and square roots generated by complex elliptic systems under a minimal regularity assumption for the coefficients.
