Hörmander Spaces, Interpolation, and Elliptic Problems
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Vladimir A. Mikhailets
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Translated by:
Peter V. Malyshev
About this book
The monograph gives a detailed exposition of the theory of general elliptic operators (scalar and matrix) and elliptic boundary value problems in Hilbert scales of Hörmander function spaces. This theory was constructed by the authors in a number of papers published in 2005–2009. It is distinguished by a systematic use of the method of interpolation with a functional parameter of abstract Hilbert spaces and Sobolev inner product spaces. This method, the theory and their applications are expounded for the first time in the monographic literature.
The monograph is written in detail and in a reader-friendly style. The complete proofs of theorems are given. This monograph is intended for a wide range of mathematicians whose research interests concern with mathematical analysis and differential equations.
Author / Editor information
V. A. Mikhailets and A. A. Murach, Institute of Mathematics of NAS of Ukraine, Kiev, Ukraine.
Supplementary Materials
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Frontmatter
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Preface
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Preface to the English edition
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Acknowledgements
vii -
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Contents
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Introduction
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Chapter 1. Interpolation and Hörmander spaces
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Chapter 2. Hörmander spaces on closed manifolds and their applications
59 -
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Chapter 3. Semihomogeneous elliptic boundary-value problems
111 -
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Chapter 4. Inhomogeneous elliptic boundary-value problems
165 -
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Chapter 5. Elliptic systems
251 -
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Bibliography
275 -
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Index
291
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