- 收听数
- 0
- 性别
- 保密
- 听众数
- 21
- 最后登录
- 2022-1-9
- QQ
 - UID
- 2264
- 阅读权限
- 40
- 帖子
- 918
- 精华
- 0
- 在线时间
- 685 小时
- 注册时间
- 2012-12-24
- 科研币
- 63
- 速递币
- 394
- 娱乐币
- 2273
- 文献值
- 29
- 资源值
- 0
- 贡献值
- 0
|
速递书局
| 封面: |
 |
| 题名: |
The Divergence Theorem and Sets of Finite Perimeter |
| 作者: |
Washek F. Pfeffer |
| 出版社: |
CRC press |
| 出版日期: |
April 12, 2012 |
| ISBN: |
9781466507197 |
| 附属页: |
齐全 |
| 书签: |
有 |
| 格式: |
清晰PDF |
| 内容简介: |
Features
•Provides new material on analysis, including geometric measure theory, bounded variation sets, and geometric topology
•Presents the important theorems from analysis, carefully developing concepts and machinery to rigorously validate the results
•Covers dyadic figures, sets of finite perimeter, and both bounded and unbounded vector fields
Summary
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. |
| 求助帖链接: |
- |
本帖子中包含更多资源
您需要 登录 才可以下载或查看，没有帐号？快速注册
-
总评分: 速递币 + 20
查看全部评分
|
发表于 2013-1-29 19:58:53
淘帖
收藏
顶
踩
