Function spaces and potential theory /
The subject of this book is the interplay between function space theory and potential theory. A crucial step in classical potential theory is the identification of the potential energy of a charge with the square of a Hilbert space norm. This leads to the Dirichlet space of locally integrable functi...
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| Format: | eBook |
| Language: | English |
| Published: |
Berlin ; New York :
Springer,
[1996]
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| Series: | Grundlehren der mathematischen Wissenschaften ;
314. |
| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
| Summary: | The subject of this book is the interplay between function space theory and potential theory. A crucial step in classical potential theory is the identification of the potential energy of a charge with the square of a Hilbert space norm. This leads to the Dirichlet space of locally integrable functions whose gradients are square integrable. More recently, a generalized potential theory has been developed, which has an analogous relationship to the standard Banach function spaces, Sobolev spaces, Besov spaces etc., that appear naturally in the study of partial differential equations. A surprisingly large part of classical potential theory has been extended to this nonlinear setting. The extensions are sometimes surprising, usually they are nontrivial and have required new methods. |
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| Item Description: | Electronic resource. |
| Physical Description: | 1 online resource (xi, 366 pages) |
| Format: | Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. |
| Bibliography: | Includes bibliographical references (pages [329]-349) and index. |
| ISBN: | 9783662032824 (electronic bk.) 3662032821 (electronic bk.) |