A Theory of Traces and the Divergence Theorem
This book provides a new approach to traces, which are viewed as linear continuous functionals on some function space. A key role in the analysis is played by integrals related to finitely additive measures, which have not previously been considered in the literature. This leads to Gauss-Green formu...
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| Main Authors: | , |
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| Formato: | Recurso Electrónico livro electrónico |
| Idioma: | inglês |
| Publicado em: |
Cham :
Springer Nature Switzerland : Imprint: Springer,
2025.
|
| Edição: | 1st ed. 2025. |
| Colecção: | Lecture Notes in Mathematics,
2372 |
| Assuntos: | |
| Acesso em linha: | https://doi.org/10.1007/978-3-031-86664-7 |
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| 100 | 1 | |a Schuricht, Friedemann. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 2 | |a A Theory of Traces and the Divergence Theorem |h [electronic resource] / |c by Friedemann Schuricht, Moritz Schönherr. |
| 250 | |a 1st ed. 2025. | ||
| 264 | 1 | |a Cham : |b Springer Nature Switzerland : |b Imprint: Springer, |c 2025. | |
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| 505 | 0 | |a - 1. Introduction -- 2. Preliminaries About Measures -- 3. Theory of Traces -- 4. Divergence Theorems. | |
| 520 | |a This book provides a new approach to traces, which are viewed as linear continuous functionals on some function space. A key role in the analysis is played by integrals related to finitely additive measures, which have not previously been considered in the literature. This leads to Gauss-Green formulas on arbitrary Borel sets for vector fields having divergence measure as well as for Sobolev and BV functions. The integrals used do not require trace functions or normal fields on the boundary and they can deal with inner boundaries. For the treatment of apparently intractable degenerate cases a second boundary integral is used. The calculus developed here also allows integral representations for the precise representative of an integrable function and for the usual boundary trace of Sobolev or BV functions. The theory presented gives a new perspective on traces for beginners as well as experts interested in partial differential equations. The integral calculus might also be a stimulating tool for geometric measure theory. | ||
| 532 | 8 | |a Accessibility summary: This PDF has been created in accordance with the PDF/UA-1 standard to enhance accessibility. It includes screen reader support, descriptions for Non-text content (such as images and graphs), bookmarks for easy navigation, keyboard-friendly links and forms, and searchable, selectable text. We recognise the importance of accessibility and welcome queries about accessibility for any of our products. If you have a question or an access need, please get in touch with us via https://www.springernature.com/gp/info/accessibility Please Note that a more accessible version of this eBook is available as an EPUB. | |
| 532 | 8 | |a Inaccessible, or known limited accessibility | |
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| 588 | |a Print version record. | ||
| 650 | 0 | |a Measure theory. | |
| 650 | 0 | |a Differential equations. | |
| 650 | 1 | 4 | |a Measure and Integration. |
| 650 | 2 | 4 | |a Differential Equations. |
| 700 | 1 | |a Schönherr, Moritz. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
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