《索伯列夫空間和插值空間導論(英文)》是以作者研究生教程的講義為藍本整理擴充而成，全面講述了索伯列夫空間和插值理論。書中包括42章，每章儘可能多的包括研究生學習所需的材料，不僅是一部研究生學習的講義材料，也是很多老師學者關心的課題。
基本介紹
- 書名：索伯列夫空間和插值空間導論
- 作者：塔塔 (Luc Tartar)
- 出版日期：2013年3月1日
- 語種：英語
- ISBN：9787510050435
- 品牌：世界圖書出版公司北京公司
- 外文名：An Introduction to Sobolev Spaces and Interpolation Spaces
- 出版社：世界圖書出版公司北京公司
- 頁數：218頁
- 開本：24
- 定價：35.00
基本介紹,內容簡介,作者簡介,圖書目錄,
基本介紹
內容簡介
《索伯列夫空間和插值空間導論(英文)》通過大量的腳註講述了本教程的形成過程有關老師的趣聞軼事，這使《索伯列夫空間和插值空間導論(英文)》不僅是一本很完善的教程，而且也非常適用於相關專業的科研人員。
作者簡介
作者：（美國）塔塔（Luc Tartar）
圖書目錄
1 historical background
2 the lebesgue measure， convolution
3 smoothing by convolution
4 truncation； radon measures； distributions
5 sobolev spaces； multiplication by smooth functions
6 density of tensor products； consequences
7 extending the notion of support
8 sobolev's embedding theorem， i ≤ p < n
9 sobolev's embedding theorem， n ≤ p≤∞
10 poincare's inequality
11 the equivalence lemma； compact embeddings
12 regularity of the boundary； consequences
13 traces on the boundary
14 green's formula
15 the fourier transform
16 traces of hs(rn)
17 proving that a point is too small
18 compact embeddings
19 lax-milgram lemma
20 the space h(div； ω)
21 background on interpolation； the complex method
22 real interpolation； k-method
23 interpolation of l2 spaces with weights
24 real interpolation； j-method
25 interpolation inequalities， the spaces (e0， e1)θ，1
26 the lions-peetre reiteration theorem
27 maximal functions
28 bilinear and nonlinear interpolation
29 obtaining lp by interpolation， with the exact norm
30 my approach to sobolev‘s embedding theorem
31 my generalization of sobolev’s embedding theorem
32 sobolev‘s embedding theorem for besov spaces
33 the lions-magenes space h1/200(ω)
34 defining sobolev spaces and besov spaces for
35 characterization of ws，p(rn)
36 characterization of ws，p
37 variants with bv spaces
38 replacing bv by interpolation spaces
39 shocks for quasi-linear hyperbolic systems
40 interpolation spaces as trace spaces
41 duality and compactness for interpolation spaces
42 miscellaneous questions
43 biographical information
44 abbreviations and mathematical notation
references
index
2 the lebesgue measure， convolution
3 smoothing by convolution
4 truncation； radon measures； distributions
5 sobolev spaces； multiplication by smooth functions
6 density of tensor products； consequences
7 extending the notion of support
8 sobolev's embedding theorem， i ≤ p < n
9 sobolev's embedding theorem， n ≤ p≤∞
10 poincare's inequality
11 the equivalence lemma； compact embeddings
12 regularity of the boundary； consequences
13 traces on the boundary
14 green's formula
15 the fourier transform
16 traces of hs(rn)
17 proving that a point is too small
18 compact embeddings
19 lax-milgram lemma
20 the space h(div； ω)
21 background on interpolation； the complex method
22 real interpolation； k-method
23 interpolation of l2 spaces with weights
24 real interpolation； j-method
25 interpolation inequalities， the spaces (e0， e1)θ，1
26 the lions-peetre reiteration theorem
27 maximal functions
28 bilinear and nonlinear interpolation
29 obtaining lp by interpolation， with the exact norm
30 my approach to sobolev‘s embedding theorem
31 my generalization of sobolev’s embedding theorem
32 sobolev‘s embedding theorem for besov spaces
33 the lions-magenes space h1/200(ω)
34 defining sobolev spaces and besov spaces for
35 characterization of ws，p(rn)
36 characterization of ws，p
37 variants with bv spaces
38 replacing bv by interpolation spaces
39 shocks for quasi-linear hyperbolic systems
40 interpolation spaces as trace spaces
41 duality and compactness for interpolation spaces
42 miscellaneous questions
43 biographical information
44 abbreviations and mathematical notation
references
index
