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Anisotropic Function Spaces Maximal Regularity for Parabolic Problems

Summary: Anisotropic Function Spaces
Maximal Regularity for Parabolic Problems
Part 1: Function Spaces
Herbert Amann
Institut f¨ur Mathematik, Universit¨at Z¨urich,
Winterthurerstr. 190, CH­8057 Z¨urich, Switzerland
2000 Mathematics Subject Classification. Primary 46E35, 58D25, 35K40, 35K50
Secondary 46E40, 42B35, 35D99, 35G10
Key words and phrases. partial differential equations, function spaces, Fourier
Abstract. In this first part of a treatise on maximal regularity for linear
parabolic systems we provide an in-depth investigation of anisotropic function
spaces. Special attention is given to trace and extension theorems on hyper-
planes and corners. Building on these results, parabolic evolution equations
in strong and weak settings will be studied in Part 2.
Acknowledgement. This work contains a detailed and widely extended ver-
sion of a series of lectures presented at the Jindrich Necas Center for Mathe-
matical Modeling in Prague, in October 2007. The author gratefully acknowl-


Source: Amann, Herbert - Institut für Mathematik, Universität Zürich


Collections: Mathematics