UID:
almahu_9947368104002882
Umfang:
1 online resource (529 p.)
ISBN:
1-283-52585-2
,
9786613838308
,
0-08-095425-1
Serie:
North-Holland mathematical library ; v. 18
Inhalt:
This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of manifolds, mappings, and Lie groups. The book will be invaluable for researchers and PhD students in differential geometry, global analysis, differential equations on manifolds, and mathematical physics, and for the readers who wish to undertake further rigorous study in this broad interdisciplinary field.
Anmerkung:
Description based upon print version of record.
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Front Cover; Interpolation Theory, Function Spaces, Differential Operators; Copyright Page; Contents; Chapter 1. Interpolation Theory in Banach Spaces; 1.1. Introduction; 1.2. General Interpolation Methods; 1.3. The K-Method; 1.4. The L-Method; 1.5. The Mean-Methods; 1.6. The J-Method; 1.7. Discrete Methods; 1.8. The Trace Method; 1.9. Complex Methods; 1.10. Reiteration Theorem; 1.11. Duality Theory; 1.12. Interpolation Theory for Quasilinearizable Interpolation Couples; 1.13. Semi-Groups of Operators and Interpolation Spaces; 1.14. Positive Operators and Interpolation Spaces
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1.15. Fractional Powers of Positive Operators and Interpolation Spaces1.16. Interpolation Properties of Entropy Ideals and Width Ideals; 1.17. Interpolation of Subspaces and Factor Spaces; 1.18. Examples and Applications; 1.19. Complements; Chapter 2. Lebesgue-Besov Spaces without Weights in Rn and R+n; 2.1. Introduction; 2.2. Integral Operators and Fourier Multipliers; 2.3. The Spaces Bisp,q(Rn), Fsp,q(Rn), Hsp(Rn), and Wsp(Rn); 2.4. Interpolation Theory for the Spaces Bsp,q(Rn) and Fsp,q(Rn); 2.5. Equivalent Norms in the Spaces Bsp,q(Rn)
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2.6. Duality Theory for the Spaces Bsp,q(Rn) and Fsp,q(Rn)2.7. The Hölder Spaces Ct(Rn); 2.8. Embedding Theorems for Different Metrics; 2.9. Direct and Inverse Embedding Theorems (Embedding on the Boundary); 2.10. The Spares Hsp(R+n) and Bsp,q(R+n); 2.11. Structure Theory; 2.12. Diversity of the Spaces Bsp,q(Rn) and Htr(Rn); 2.13. Anisotropic Spaces; Chapter 3. Lebesgue-Besov Spaces with Weigths in Domains; 3.1. Introduction; 3.2. Definitions and Fundamental Properties; 3.3. Interpolation Theory for the Spaces Wmp(O; s); 3.4. Interpolation Theory for the Spaces Bsp,q(O; Qu; Qv) and Hsp(O
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QuQv); 3.5. Embedding Theorems for Different Metrics; 3.6. Direct and Inverse Embedding Theorems (Embedding on the Boundary); 3.7. Structure Theory; 3.8. Embedding Operators and Width Numbers; 3.9. The Spaces wsp,u(Rn); 3.10. Complements; Chapter 4. Lebesgue-Besov Spaces without Weigths in Domains; 4.1. Introduction; 4.2. Definitions, Extension Theorems; 4.3. Interpolation Theory; 4.4. Equivalent Norms in Sobolev-Besov Spaces; 4.5. The Holder Spaces Ct'(O); 4.6. Embedding Theorems for Different Metrics, Inclusion Properties
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4.7. Direct and Inverse Embedding Theorems (Embedding on the Boundary)4.8. Duality Theory; 4.9. Structure Theory; 4.10. Qualitative Roperties of Embedding Operators; 4.11. Complements; Chapter 5. Regular Elliptic Differential Operators; 5.1. Introduction; 5.2. Regular Elliptic Differential Operators; 5.3. A-Priori-Estimates; 5.4. Lp-Theory in Sobolev Spaces; 5.5. Boundary Value Problems [Part I]; 5.6. Distributions of Eigenvalues, Associated Eigenvectors, and Green Functions; 5.7. Boundary Value Problems [Part II]; Chapter 6. Strongly Degenerate Elliptic Differential Operators
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6.1. Introduction
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English
Weitere Ausg.:
ISBN 0-7204-0710-9
Sprache:
Englisch
