Linear and quasilinear evolution equations in the context of weighted $L_p$-spaces

TL;DR

This paper surveys key results on maximal regularity for evolution equations in weighted $L_p$-spaces and demonstrates their applications to semilinear and quasilinear parabolic equations.

Contribution

It provides a comprehensive overview of Prüss and Simonett's 2004 results and highlights their applications to complex evolution equations.

Findings

Maximal regularity results in weighted $L_p$-spaces are effective for parabolic equations.

Applications include well-posedness of semilinear and quasilinear problems.

The survey illustrates the power of these methods in evolution equations.

Abstract

In 2004, the article "Maximal regularity for evolution equations in weighted $L_p$-spaces" by J. Pr\"{u}ss and G. Simonett 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.