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Published in:
The Work of Yoshihiro Shibata Read chapter Read first chapter

2016 | OriginalPaper | Chapter

Inhomogeneous Boundary Value Problems in Spaces of Higher Regularity

Authors : Robert Denk, Tim Seger

Published in: Recent Developments of Mathematical Fluid Mechanics

Publisher: Springer Basel

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Abstract

Uniform a priori estimates for parameter-elliptic boundary value problems are well-known if the underlying basic space equals \(L^{p}(\Omega )\). However, much less is known for the \(W_{p}^{s}(\Omega )\)-realization, s > 0, of a parameter-elliptic boundary value problem. We discuss a priori estimates and the generation of analytic semigroups for these realizations in various cases. The Banach scale method can be applied for homogeneous boundary conditions if the right-hand side satisfies certain compatibility conditions, while for the general case parameter-dependent norms are used. In particular, we obtain a resolvent estimate for the general situation where no analytic semigroup is generated.

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previous chapter On Unsteady Internal Flows of Bingham Fluids Subject to Threshold Slip on the Impermeable Boundary
next chapter Blow-Up Criterion for 3D Navier-Stokes Equations and Landau-Lifshitz System in a Bounded Domain
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Metadata
Title
Inhomogeneous Boundary Value Problems in Spaces of Higher Regularity
Authors
Robert Denk
Tim Seger
Copyright Year
2016
Publisher
Springer Basel
Book
Recent Developments of Mathematical Fluid Mechanics

Print ISBN: 978-3-0348-0938-2

Electronic ISBN: 978-3-0348-0939-9

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-0348-0939-9_9

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