| Description |
1 online resource (ix, 101 pages) |
| Series |
Memoirs of the American Mathematical Society, 1947-6221 ; v. 688 |
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Memoirs of the American Mathematical Society ; no. 688. 0065-9266
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| Contents |
1. Introduction 2. What are Poincaré and Sobolev inequalities? 3. Poincaré inequalities, pointwise estimates, and Sobolev classes 4. Examples and necessary conditions 5. Sobolev type inequalities by means of Riesz potentials 6. Trudinger inequality 7. A version of the Sobolev embedding theorem on spheres 8. Rellich-Kondrachov 9. Sobolev classes in John domains 10. Poincaré inequality: examples 11. Carnot-Carathéodory spaces 12. Graphs 13. Applications to P.D.E and nonlinear potential theory 14. Appendix |
| Summary |
There are several generalizations of the classical theory of Sobolev spaces as they are necessary for the applications to Carnot-Caratheodory spaces, subelliptic equations, quasiconformal mappings on Carnot groups and more general Loewner spaces, analysis on topological manifolds, potential theory on infinite graphs, analysis on fractals and the theory of Dirichlet forms. The aim of this paper is to present a unified approach to the theory of Sobolev spaces that covers applications to many of those areas. The variety of different areas of applications forces a very general setting |
| Notes |
"May 2000, volume 145, number 688 (first of 4 numbers)." |
| Bibliography |
Includes bibliographical references (pages 89-101) |
| Notes |
Print version record |
| Subject |
Sobolev spaces.
|
|
Inequalities (Mathematics)
|
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Inequalities (Mathematics)
|
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Sobolev spaces
|
| Form |
Electronic book
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| Author |
Koskela, Pekka
|
| ISBN |
9781470402792 |
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1470402793 |
|
