非光滑拟线性抛物系统的非自治极大抛物正则性
Nonautonomous maximal parabolic regularity for nonsmooth quasilinear parabolic systems
AI总结：
本文针对非光滑域上带混合边界条件的非自治拟线性抛物系统，建立了$L^p$-极大正则性，通过外推技术获得一致估计，仅需温和边界正则性及有界可测复系数，并允许时间非局部非线性，涵盖稳态不满足椭圆性的情形。
AI中文摘要：
本文研究抽象非自治抛物系统及其在带混合边界条件的负Sobolev空间中的拟线性对应物的$L^p$-极大抛物正则性。我们的结果是在具有混合边界条件的非光滑区域中通过外推技术推导出来的，该技术还产生了抛物解算子的一致估计。我们仅要求非常温和的边界正则性，不要求Lipschitz类，并且通常仅要求有界且可测的复系数。拟线性公式中的非线性函数可以在时间上是非局部的；这也允许考虑某些其稳态对应物不满足通常椭圆性条件的系统。
英文摘要：
In this paper we are concerned with $L^p$-maximal parabolic regularity for abstract nonautonomous parabolic systems and their quasilinear counterpart in negative Sobolev spaces incorporating mixed boundary conditions. Our results are derived in the setting of nonsmooth domains with mixed boundary conditions by an extrapolation technique which also yields uniform estimates for the parabolic solution operators. We require only very mild boundary regularity, not in the Lipschitz-class, and generally only bounded and measurable complex coefficients. The nonlinear functions in the quasilinear formulation can be nonlocal-in-time; this allows also to consider certain systems whose stationary counterpart fails to satisfy the usual ellipticity conditions.
