In 2004, the article Maximal regularity for evolution equations in weighted \(L_p\)-spaces by Prüss and Simonett (Arch Math 82:415–431, 2004) has been published in Archiv der Mathematik. We provide a survey of the main results of that article and outline some applications to semilinear and quasilinear parabolic evolution equations which illustrate their power.

中文翻译：

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加权 $$L_p$$ 空间中的线性和拟线性演化方程

2004 年，Prüss 和 Simonett 的文章《Maximalregularity for evolutionequations in Weighted \(L_p\) - space》（Arch Math 82:415–431, 2004）发表在Archiv der Mathematik上。我们对该文章的主要结果进行了调查，并概述了半线性和拟线性抛物型演化方程的一些应用，以说明其威力。