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  1. Bog
  2. Fysik
  3. Matematisk fysik
The Divergence Theorem and Sets of Finite Perimeter
Af: Washek F. Pfeffer
Engelsk
Bogcover for The Divergence Theorem and Sets of Finite Perimeter af Washek F. Pfeffer, 9780367381516
Specifikationer
Sprog:
Engelsk
Sider:
259
ISBN-13:
9780367381516
Indbinding:
Paperback
ISBN-10:
0367381516
Kategori:
Udg. Dato:
5 sep 2019
Størrelse i cm:
23,4 x 15,6
Forlag:
Oplagsdato:
5 sep 2019
Forfatter(e):
Genre:

The Divergence Theorem and Sets of Finite Perimeter

Af: Washek F. Pfeffer
Engelsk
Paperback 2019
Format:
Paperback
Bog beskrivelse

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.

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Specifikationer
Sprog:
Engelsk
Sider:
259
ISBN-13:
9780367381516
Indbinding:
Paperback
ISBN-10:
0367381516
Kategori:
Udg. Dato:
5 sep 2019
Størrelse i cm:
23,4 x 15,6
Forlag:
Oplagsdato:
5 sep 2019
Forfatter(e):
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