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• W3012324347 abstract "In this note, we give an introduction to the concept of maximal $L^p$-regularity as a method to solve nonlinear partial differential equations. We first define maximal regularity for autonomous and non-autonomous problems and describe the connection to Fourier multipliers and $mathcal R$-boundedness. The abstract results are applied to a large class of parabolic systems in the whole space and to general parabolic boundary value problems. For this, both the construction of solution operators for boundary value problems and a characterization of trace spaces of Sobolev spaces are discussed. For the nonlinear equation, we obtain local in time well-posedness in appropriately chosen Sobolev spaces. This manuscript is based on known results and consists of an extended version of lecture notes on this topic." @default.
• W3012324347 created "2020-03-23" @default.
• W3012324347 creator A5072903057 @default.
• W3012324347 date "2020-03-10" @default.
• W3012324347 modified "2023-09-27" @default.
• W3012324347 title "An introduction to maximal regularity for parabolic evolution equations" @default.
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• W3012324347 hasPublicationYear "2020" @default.
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