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The theory of Lebesgue and Sobolev spaces with variable integrability is experiencing a steady expansion, and is the subject of much vigorous research by functional analysts, function-space analysts and specialists in nonlinear analysis. These spaces have attracted attention not only because of their intrinsic mathematical importance as natural, interesting examples of non-rearrangement-invariant function spaces but also in view of their applications, which include the mathematical modeling of electrorheological fluids and image restoration. The main focus of this book is to provide a solid functional-analytic background for the study of differential operators on spaces with variable integrability. It includes some novel stability phenomena which the authors have recently discovered. At the present time, this is the only book which focuses systematically on differential operators on spaces with variable integrability. The authors present a concise, natural introduction to the basic material and steadily move toward differential operators on these spaces, leading the reader quickly to current research topics.
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Showing 3 featured editions. View all 3 editions?
Edition | Availability |
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1
Differential Operators on Spaces of Variable Integrability
2014, World Scientific Publishing Co Pte Ltd
in English
1322030731 9781322030739
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WorldCat
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2
Differential Operators on Spaces of Variable Integrability
2014, World Scientific Publishing Co Pte Ltd
in English
9814596329 9789814596329
|
zzzz
Libraries near you:
WorldCat
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3
Differential Operators on Spaces of Variable Integrability
June 26, 2014, World Scientific Publishing Company (WSPC)
Paperback
in English
- First edition
9814596310 9789814596312
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Book Details
Edition Notes
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Preliminaries. 1.1. The geometry of Banach spaces. 1.2. Spaces with variable exponent --
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Sobolev spaces with variable exponent. 2.1. Definition and functional-analytic properties. 2.2. Sobolev embeddings. 2.3. Compact embeddings. 2.4. Riesz potentials. 2.5. Poincare-type inequalities. 2.6. Embeddings. 2.7. Holder spaces with variable exponents. 2.8. Compact embeddings revisited --
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The p[symbol]-Laplacian. 3.1. Preliminaries. 3.2. The p[symbol]-Laplacian. 3.3. Stability with respect to integrability --
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Eigenvalues. 4.1. The derivative of the modular. 4.2. Compactness and Eigenvalues. 4.3. Modular Eigenvalues. 4.4. Stability with respect to the exponent. 4.5. Convergence properties of the Eigenfunctions --
- Approximation on Lp spaces. 5.1. s-numbers and n-widths. 5.2. A Sobolev embedding. 5.3. Integral operators.
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