Differential operators on spaces of variable integrability /:
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 thei...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
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New Jersey :
World Scientific,
[2014]
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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. |
| Beschreibung: | 1 online resource (xiv, 208 pages) |
| Bibliographie: | Includes bibliographical references (pages 197-201) and indexes. |
| ISBN: | 9789814596329 9814596329 |
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| 505 | 0 | |a 1. Preliminaries. 1.1. The geometry of Banach spaces. 1.2. Spaces with variable exponent -- 2. 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 -- 3. The p[symbol]-Laplacian. 3.1. Preliminaries. 3.2. The p[symbol]-Laplacian. 3.3. Stability with respect to integrability -- 4. 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 -- 5. Approximation on Lp spaces. 5.1. s-numbers and n-widths. 5.2. A Sobolev embedding. 5.3. Integral operators. | |
| 520 | |a 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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| author | Edmunds, D. E. (David Eric) Lang, Jan Mendez, Osvaldo (Osvaldo David) |
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| contents | 1. Preliminaries. 1.1. The geometry of Banach spaces. 1.2. Spaces with variable exponent -- 2. 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 -- 3. The p[symbol]-Laplacian. 3.1. Preliminaries. 3.2. The p[symbol]-Laplacian. 3.3. Stability with respect to integrability -- 4. 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 -- 5. Approximation on Lp spaces. 5.1. s-numbers and n-widths. 5.2. A Sobolev embedding. 5.3. Integral operators. |
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| indexdate | 2024-11-27T13:26:07Z |
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| spelling | Edmunds, D. E. (David Eric), author. http://id.loc.gov/authorities/names/n78010216 Differential operators on spaces of variable integrability / David E. Edmunds, University of Sussex, UK, Jan Lang, the Ohio State University, USA, Osvaldo Mendez, the University of Texas at El Paso, USA. New Jersey : World Scientific, [2014] ©2014 1 online resource (xiv, 208 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Includes bibliographical references (pages 197-201) and indexes. Print version record. 1. Preliminaries. 1.1. The geometry of Banach spaces. 1.2. Spaces with variable exponent -- 2. 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 -- 3. The p[symbol]-Laplacian. 3.1. Preliminaries. 3.2. The p[symbol]-Laplacian. 3.3. Stability with respect to integrability -- 4. 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 -- 5. Approximation on Lp spaces. 5.1. s-numbers and n-widths. 5.2. A Sobolev embedding. 5.3. Integral operators. 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. Function spaces. http://id.loc.gov/authorities/subjects/sh85052310 Sobolev spaces. http://id.loc.gov/authorities/subjects/sh85123836 Differential operators. http://id.loc.gov/authorities/subjects/sh85037921 Espaces fonctionnels. Espaces de Sobolev. Opérateurs différentiels. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Differential operators fast Function spaces fast Sobolev spaces fast Lang, Jan, author. Mendez, Osvaldo (Osvaldo David), author. http://id.loc.gov/authorities/names/n2014022080 has work: Differential operators on spaces of variable integrability (Text) https://id.oclc.org/worldcat/entity/E39PCGJBhC9VbgrqT3tM8rFqHy https://id.oclc.org/worldcat/ontology/hasWork Print version: Edmunds, D.E. (David Eric). Differential operators on spaces of variable integrability. New Jersey : World Scientific, 2014 9789814596312 (DLC) 2014015285 (OCoLC)871789716 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=824747 Volltext |
| spellingShingle | Edmunds, D. E. (David Eric) Lang, Jan Mendez, Osvaldo (Osvaldo David) Differential operators on spaces of variable integrability / 1. Preliminaries. 1.1. The geometry of Banach spaces. 1.2. Spaces with variable exponent -- 2. 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 -- 3. The p[symbol]-Laplacian. 3.1. Preliminaries. 3.2. The p[symbol]-Laplacian. 3.3. Stability with respect to integrability -- 4. 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 -- 5. Approximation on Lp spaces. 5.1. s-numbers and n-widths. 5.2. A Sobolev embedding. 5.3. Integral operators. Function spaces. http://id.loc.gov/authorities/subjects/sh85052310 Sobolev spaces. http://id.loc.gov/authorities/subjects/sh85123836 Differential operators. http://id.loc.gov/authorities/subjects/sh85037921 Espaces fonctionnels. Espaces de Sobolev. Opérateurs différentiels. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Differential operators fast Function spaces fast Sobolev spaces fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85052310 http://id.loc.gov/authorities/subjects/sh85123836 http://id.loc.gov/authorities/subjects/sh85037921 |
| title | Differential operators on spaces of variable integrability / |
| title_auth | Differential operators on spaces of variable integrability / |
| title_exact_search | Differential operators on spaces of variable integrability / |
| title_full | Differential operators on spaces of variable integrability / David E. Edmunds, University of Sussex, UK, Jan Lang, the Ohio State University, USA, Osvaldo Mendez, the University of Texas at El Paso, USA. |
| title_fullStr | Differential operators on spaces of variable integrability / David E. Edmunds, University of Sussex, UK, Jan Lang, the Ohio State University, USA, Osvaldo Mendez, the University of Texas at El Paso, USA. |
| title_full_unstemmed | Differential operators on spaces of variable integrability / David E. Edmunds, University of Sussex, UK, Jan Lang, the Ohio State University, USA, Osvaldo Mendez, the University of Texas at El Paso, USA. |
| title_short | Differential operators on spaces of variable integrability / |
| title_sort | differential operators on spaces of variable integrability |
| topic | Function spaces. http://id.loc.gov/authorities/subjects/sh85052310 Sobolev spaces. http://id.loc.gov/authorities/subjects/sh85123836 Differential operators. http://id.loc.gov/authorities/subjects/sh85037921 Espaces fonctionnels. Espaces de Sobolev. Opérateurs différentiels. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Differential operators fast Function spaces fast Sobolev spaces fast |
| topic_facet | Function spaces. Sobolev spaces. Differential operators. Espaces fonctionnels. Espaces de Sobolev. Opérateurs différentiels. MATHEMATICS Calculus. MATHEMATICS Mathematical Analysis. Differential operators Function spaces Sobolev spaces |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=824747 |
| work_keys_str_mv | AT edmundsde differentialoperatorsonspacesofvariableintegrability AT langjan differentialoperatorsonspacesofvariableintegrability AT mendezosvaldo differentialoperatorsonspacesofvariableintegrability |