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Critical spaces for quasilinear parabolic evolution equations and applications

Prüss, Jan ; Simonett, Gieri ; Wilke, Mathias



Abstract

We present a comprehensive theory of critical spaces for the broad class of quasilinear parabolic evolution equations. The approach is based on maximal L-p-regularity in time-weighted function spaces. It is shown that our notion of critical spaces coincides with the concept of scaling invariant spaces in case that the underlying partial differential equation enjoys a scaling invariance. ...

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