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The Divergence Theorem and Sets of Finite Perimeter
This book is devoted to a detailed development of the divergence theorem. The framework is that of Lebesgue integration -- no generalized Riemann integrals of Henstock--Kurzweil variety are involved. In Part I the divergence theorem is established by a combinatorial argument involving dyadic cubes....
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Lenguaje: | eng |
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CRC Press
2012
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Acceso en línea: | http://cds.cern.ch/record/1486752 |
_version_ | 1780926172087975936 |
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author | Pfeffer, Washek F |
author_facet | Pfeffer, Washek F |
author_sort | Pfeffer, Washek F |
collection | CERN |
description | This book is devoted to a detailed development of the divergence theorem. The framework is that of Lebesgue integration -- no generalized Riemann integrals of Henstock--Kurzweil variety are involved. In Part I the divergence theorem is established by a combinatorial argument involving dyadic cubes. Only elementary properties of the Lebesgue integral and Hausdorff measures are used. The resulting integration by parts is sufficiently general for many applications. As an example, it is applied to removable singularities of Cauchy--Riemann, Laplace, and minimal surface equations. The sets of finit |
id | cern-1486752 |
institution | Organización Europea para la Investigación Nuclear |
language | eng |
publishDate | 2012 |
publisher | CRC Press |
record_format | invenio |
spelling | cern-14867522021-04-22T00:16:01Zhttp://cds.cern.ch/record/1486752engPfeffer, Washek FThe Divergence Theorem and Sets of Finite PerimeterMathematical Physics and Mathematics This book is devoted to a detailed development of the divergence theorem. The framework is that of Lebesgue integration -- no generalized Riemann integrals of Henstock--Kurzweil variety are involved. In Part I the divergence theorem is established by a combinatorial argument involving dyadic cubes. Only elementary properties of the Lebesgue integral and Hausdorff measures are used. The resulting integration by parts is sufficiently general for many applications. As an example, it is applied to removable singularities of Cauchy--Riemann, Laplace, and minimal surface equations. The sets of finitCRC Pressoai:cds.cern.ch:14867522012 |
spellingShingle | Mathematical Physics and Mathematics Pfeffer, Washek F The Divergence Theorem and Sets of Finite Perimeter |
title | The Divergence Theorem and Sets of Finite Perimeter |
title_full | The Divergence Theorem and Sets of Finite Perimeter |
title_fullStr | The Divergence Theorem and Sets of Finite Perimeter |
title_full_unstemmed | The Divergence Theorem and Sets of Finite Perimeter |
title_short | The Divergence Theorem and Sets of Finite Perimeter |
title_sort | divergence theorem and sets of finite perimeter |
topic | Mathematical Physics and Mathematics |
url | http://cds.cern.ch/record/1486752 |
work_keys_str_mv | AT pfefferwashekf thedivergencetheoremandsetsoffiniteperimeter AT pfefferwashekf divergencetheoremandsetsoffiniteperimeter |