Divergence Theorem and Sets of Finite Perimeter

AvWashek F. Pfeffer

E-bok

PDF, Engelska, 2016

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Beskrivning

This book presents a detailed development of the divergence theorem. The framework is that of Lebesgue integration-no generalized Riemann integrals of Henstock-Kurzweil variety are involved. The first part of the book establishes the divergence theorem by a combinatorial argument involving dyadic cubes. Only elementary properties of the Lebesgue integral and Hausdorff measures are used. The second part introduces the sets of finite perimeter and the last part proves the general divergence theorem for bounded vector fields.

Produktinformation

Utgivningsdatum:2016-02-03
Språk:Engelska
Filformat:PDF
Kopieringsskydd:LCP
ISBN:9781466507210
Förlag:Taylor & Francis Inc

Utforska kategorier

Beräkning och matematisk analys inom Naturvetenskap och teknik

Recensioner i media

"The intentions of the author connected with the entire monograph are best illustrated by a quotation from the introduction: 'We divide the problem into three parts. (1) Extending the family of vector fields for which the divergence theorem holds on simple sets. (2) Extending the family of sets for which the divergence theorem holds for Lipschitz vector fields. (3) Proving the divergence theorem when the vector fields and sets are extended simultaneously.' ... The last chapter ... [contain] results published for the first time in this century. The author starts these considerations with a nice presentation of the background of these problems." -Ryszard J. Pawlak, Mathematical Reviews, April 2013

Innehållsförteckning

DYADIC FIGURES: Preliminaries. Divergence Theorem for Dyadic Figures. Removable Singularities. SETS OF FINITE PERIMETER: Perimeter. BV Functions. Locally BV Sets. THE DIVERGENCE THEOREM: Bounded Vector Fields. Unbounded Vector Fields. Mean Divergence. Charges. The Divergence Equation.