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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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Autor principal: Pfeffer, Washek F
Lenguaje:eng
Publicado: CRC Press 2012
Materias:
Acceso en línea:http://cds.cern.ch/record/1486752
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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
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publishDate 2012
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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
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