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

0 avg rating
( 0 ratings by Goodreads )
 
9781466507197: The Divergence Theorem and Sets of Finite Perimeter (Chapman & Hall/CRC Pure and Applied 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 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.

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

Review:

"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

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

Top Search Results from the AbeBooks Marketplace

International Edition
International Edition

1.

Washek F. Pfeffer
ISBN 10: 1466507195 ISBN 13: 9781466507197
New Hardcover Quantity Available: 5
International Edition
Seller:
PRIORITY BOOKS
(Springfield, VA, U.S.A.)
Rating
[?]

Book Description Hardcover. Book Condition: New. HARDCOVER Book, New Condition, Fast Shipping. Ready in Stock. 1st Edition. [Please Read Carefully Before Buying], This Is An International Edition. Printed In Black and White. 259 Pages, Book Cover And ISBN No May Be Different From US Edition. Restricted Sales Disclaimer Wordings Not For Sales In USA And Canada May Be Printed On The Cover Of The Book. Standard Shipping 7-14 Business Days. Expedited Shiping 4-8 Business Days. ***WE DO NOT ENTERTAIN BULK ORDERS.*** The Books May Be Ship From Overseas For Inventory Purpose. Bookseller Inventory # 402744

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 82.67
Convert Currency

Add to Basket

Shipping: US$ 3.99
Within U.S.A.
Destination, Rates & Speeds

2.

Pfeffer, Washek F.
Published by Chapman and Hall/CRC (2012)
ISBN 10: 1466507195 ISBN 13: 9781466507197
New Hardcover Quantity Available: 2
Seller:
Murray Media
(North Miami Beach, FL, U.S.A.)
Rating
[?]

Book Description Chapman and Hall/CRC, 2012. Hardcover. Book Condition: New. Never used!. Bookseller Inventory # P111466507195

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 84.73
Convert Currency

Add to Basket

Shipping: US$ 1.99
Within U.S.A.
Destination, Rates & Speeds
International Edition
International Edition

3.

Washek F. Pfeffer
ISBN 10: 1466507195 ISBN 13: 9781466507197
New Hardcover Quantity Available: 1
International Edition
Seller:
Nick Book House
(Fresno, CA, U.S.A.)
Rating
[?]

Book Description Hardcover. Book Condition: New. New, HARDCOVER International Edition, Printed in Black and White, Different ISBN, Same Content As US edition, Book Cover may be Different, in English Language. Bookseller Inventory # 26439

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 82.77
Convert Currency

Add to Basket

Shipping: US$ 3.99
Within U.S.A.
Destination, Rates & Speeds

4.

Pfeffer
Published by Taylor & Francis (2015)
ISBN 10: 1466507195 ISBN 13: 9781466507197
New Hardcover Quantity Available: 2
Seller:
Books in my Basket
(New Delhi, India)
Rating
[?]

Book Description Taylor & Francis, 2015. Hardcover. Book Condition: New. Bookseller Inventory # 328304

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 99.90
Convert Currency

Add to Basket

Shipping: US$ 4.86
From India to U.S.A.
Destination, Rates & Speeds

5.

Washek F. Pfeffer
ISBN 10: 1466507195 ISBN 13: 9781466507197
New Quantity Available: 1
Seller:
Speedy Hen LLC
(Sunrise, FL, U.S.A.)
Rating
[?]

Book Description Book Condition: New. Bookseller Inventory # ST1466507195. Bookseller Inventory # ST1466507195

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 107.56
Convert Currency

Add to Basket

Shipping: FREE
Within U.S.A.
Destination, Rates & Speeds

6.

Washek F. Pfeffer
Published by Taylor Francis Inc, United States (2015)
ISBN 10: 1466507195 ISBN 13: 9781466507197
New Hardcover Quantity Available: 1
Seller:
The Book Depository US
(London, United Kingdom)
Rating
[?]

Book Description Taylor Francis Inc, United States, 2015. Hardback. Book Condition: New. New.. Language: English . Brand New Book. 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. Bookseller Inventory # AA69781466507197

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 107.80
Convert Currency

Add to Basket

Shipping: FREE
From United Kingdom to U.S.A.
Destination, Rates & Speeds

7.

Washek F. Pfeffer
Published by Chapman and Hall/CRC (2012)
ISBN 10: 1466507195 ISBN 13: 9781466507197
New Quantity Available: 4
Seller:
Books2Anywhere
(Fairford, GLOS, United Kingdom)
Rating
[?]

Book Description Chapman and Hall/CRC, 2012. HRD. Book Condition: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Bookseller Inventory # FT-9781466507197

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 98.54
Convert Currency

Add to Basket

Shipping: US$ 12.07
From United Kingdom to U.S.A.
Destination, Rates & Speeds

8.

Washek F. Pfeffer
Published by Taylor Francis Inc, United States (2012)
ISBN 10: 1466507195 ISBN 13: 9781466507197
New Hardcover Quantity Available: 1
Seller:
The Book Depository
(London, United Kingdom)
Rating
[?]

Book Description Taylor Francis Inc, United States, 2012. Hardback. Book Condition: New. New.. Language: English . Brand New Book. 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. Bookseller Inventory # AA69781466507197

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 110.97
Convert Currency

Add to Basket

Shipping: FREE
From United Kingdom to U.S.A.
Destination, Rates & Speeds

9.

Pfeffer, Washek F.
ISBN 10: 1466507195 ISBN 13: 9781466507197
New Quantity Available: 3
Seller:
Paperbackshop-US
(Wood Dale, IL, U.S.A.)
Rating
[?]

Book Description 2012. HRD. Book Condition: New. New Book. Shipped from US within 10 to 14 business days. Established seller since 2000. Bookseller Inventory # VT-9781466507197

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 110.63
Convert Currency

Add to Basket

Shipping: US$ 3.99
Within U.S.A.
Destination, Rates & Speeds

10.

Washek F. Pfeffer
Published by Taylor and Francis 2012-05-11, Boca Raton (2012)
ISBN 10: 1466507195 ISBN 13: 9781466507197
New Hardcover Quantity Available: 1
Seller:
Blackwell's
(Oxford, OX, United Kingdom)
Rating
[?]

Book Description Taylor and Francis 2012-05-11, Boca Raton, 2012. hardback. Book Condition: New. Bookseller Inventory # 9781466507197

More Information About This Seller | Ask Bookseller a Question

Buy New
US$ 114.62
Convert Currency

Add to Basket

Shipping: US$ 8.05
From United Kingdom to U.S.A.
Destination, Rates & Speeds

There are more copies of this book

View all search results for this book