The Divergence Theorem and Sets of Finite Perimeter

Washek F. Pfeffer

ISBN 10: 0367381516 / ISBN 13: 9780367381516

Editore: Chapman And Hall/CRC, 2019

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nach der Bestellung gedruckt Neuware - Printed after ordering - 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.

Codice articolo 9780367381516

Dati bibliografici

• Titolo: The Divergence Theorem and Sets of Finite Perimeter
• Editore: Chapman And Hall/CRC
• Data di pubblicazione: 2019
• Lingua: Inglese
• ISBN 10: 0367381516
• ISBN 13: 9780367381516
• Rilegatura: Taschenbuch
• Condizione: Neu
• Dimensioni: 234 L x 156 A x 14 P (millimetri) 234 millimetri di larghezza per 156 millimetri di altezza per 14 millimetri di profondità
• Peso: 401 grammi

Descrizione articolo

Riassunto

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 finite perimeter are introduced in Part II. Both the geometric and analytic points of view are presented. The equivalence of these viewpoints is obtained via the functions of bounded variation. These functions are studied in a self-contained manner with no references to Sobolev’s spaces. The coarea theorem provides a link between the sets of finite perimeter and functions of bounded variation.

The general divergence theorem for bounded vector fields is proved in Part III. The proof consists of adapting the combinatorial argument of Part I to sets of finite perimeter. The unbounded vector fields and mean divergence are also discussed. The final chapter contains a characterization of the distributions that are equal to the flux of a continuous vector field.

Informazioni sull?autore

Pfeffer, Washek F.