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.

About the Author:

Pfeffer, Washek F.

"About this title" may belong to another edition of this title.

Store Description

Quality books, speedy shipping, and great customer service! Please note that used items may not include access codes or cards, CD's or other accessories, regardless of what is stated in item title. If you need to guarantee that these items are included, please purchase a brand new copy.

Visit Seller's Storefront

Seller's business information

J2B Holdings, LLC
13770 NOEL RD, #803600, Dallas, TX, 75240, U.S.A.

Terms of Sale:

We guarantee the condition of every book as it's described on the AbeBooks web
sites. Please note that used items may not include access codes or cards, CD's
or other accessories, regardless of what is stated in item title. If you need to
guarantee that these items are included, please purchase a brand new copy.

All requests for refunds and/or returns will be processed in accordance with
AbeBooks policies. If you're dissatisfied with your purchase (Incorrect Book/Not
as Described/Damaged) or if ...

More Information

Shipping Terms:

Books ordered via expedited shipping should arrive between 2 and 7 business days after shipment confirmation. Books ordered via standard shipping should arrive between 4 and 14 business days after shipment confirmation.

Payment Methods
accepted by seller

Add to Wants

Items related to The Divergence Theorem and Sets of Finite Perimeter...

The Divergence Theorem and Sets of Finite Perimeter (Chapman & Hall/CRC Pure and Applied Mathematics)

Pfeffer, Washek F.

New - Soft cover

Seller's business information