Herbert Amann

Linear and Quasilinear Parabolic Problems (eBook, PDF)

Volume II: Function Spaces

• Format: PDF

Produktbeschreibung

This volume discusses an in-depth theory of function spaces in an Euclidean setting, including several new features, not previously covered in the literature. In particular, it develops a unified theory of anisotropic Besov and Bessel potential spaces on Euclidean corners, with infinite-dimensional Banach spaces as targets.

It especially highlights the most important subclasses of Besov spaces, namely Slobodeckii and Hölder spaces. In this case, no restrictions are imposed on the target spaces, except for reflexivity assumptions in duality results. In this general setting, the author proves sharp embedding, interpolation, and trace theorems, point-wise multiplier results, as well as Gagliardo-Nirenberg estimates and generalizations of Aubin-Lions compactness theorems.

The results presented pave the way for new applications in situations where infinite-dimensional target spaces are relevant - in the realm of stochastic differential equations, for example.

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Produktdetails

• Verlag: Springer Nature Switzerland
• Seitenzahl: 462
• Erscheinungstermin: 16. April 2019
• Englisch
• ISBN-13: 9783030117634
• Artikelnr.: 56319349

Inhaltsangabe

Notations and Conventions.- 1 Topological Spaces.- 2 Locally Convex Spaces.- 3 Complexifications.- 4 Unbounded Linear Operators.- 5 General Conventions.- I Generators and Interpolation.- 1 Generators of Analytic Semigroups.- 2 Interpolation Functors.- II Cauchy Problems and Evolution Operators.- 1 Linear Cauchy Problems.- 2 Parabolic Evolution Operators.- 3 Linear Volterra Integral Equations.- 4 Existence of Evolution Operators.- 5 Stability Estimates.- 6 Invariance and Positivity.- III Maximal Regularity.- 1 General Principles.- 2 Maximal Hölder Regularity.- 3 Maximal Continuous Regularity.- 4 Maximal Sobolev Regularity.- IV Variable Domains.- 1 Higher Regularity.- 2 Constant Interpolation Spaces.- 3 Maximal Regularity.- V Scales of Banach Spaces.- 1 Banach Scales.- 2 Evolution Equations in Banach Scales.- List of Symbols.