退化抛物方程

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作　者：	（美）德贝内代托著
出版社：	世界图书出版公司
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标　签：	微积分

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ISBN：	9787510004766	出版时间：	2010-01-01	包装：	平装
开本：	24开	页数：	387	字数：

内容简介

　　数学真正意义上研究退化和奇异抛物偏微分方程是近些年才开始的，起源于60年代中叶DeGiorgi，Moser，Ladyzenskajia和Ural’tzeva这些人的工作。本书是近些年来该领域的进展的综述。其基本思想来自上个世纪90年代作者在波恩大学的Lipschitz讲义。目次：函数空间；弱解和局部能量估计；退化抛物方程的Holder连续性；奇异抛物方程解的Holder连续性；弱解有界性；Harnack 估计：p]2；Harnack 估计和；退化和奇异抛物系统；抛物p系统：Du的Holder连续性；抛物p系统：边界奇异；ΣT中的非负解：p]2； ΣT中的非负解：1[p[2。本书适用于数学专业的研究生和科研人员。

作者简介

暂缺《退化抛物方程》作者简介

图书目录

Preface
1. Elliptic equations： Harnack estimates and Holder continuity ...
2. Parabolic equations： Hamack estimates and holder continuity ..
3. Parabolic equations and systems
4. Main results
I. Notation and function spaces
1. Some notation
2. Basic facts about
3. Parabolic spaces and embeddings
4. Auxiliary lemmas
5. Bibliographical notes
II. Weak solutions and local energy estimates
1. Quasilinear degenerate or singular equations
2. Boundary value problems
3. Local integral inequalities
4. Energy estimates near the boundary
5. Restricted structures： the levels k and the constant 7
6. Bibliographical notes
III. Holder continuity of solutions of degenerate parabolic equations
1. The regularity theorem
2. Preliminaries
3. The main proposition
4. The first alternative
5. The first alternative continued
6. The first alternative concluded
7. The second alternative
8. The second alternative continued
9. The second alternative concluded
10. Proof of Proposition 3.1
11. Regularity up to t = 0
12. Regularity up to ST. Dirichlet data
13. Regularity at ST. Variational data
14. Remarks on stability
15. Bibliographical notes
IV. Holder continuity of solutions of singular parabolic equations
1. Singular equations and the regularity theorems
2. The main proposition
3. Preliminaries
4. Rescaled iterations
5. The first alternative
6. Proof of Lemma 5.1. Integral inequalities
7. An auxiliary proposition
8. Proof of Proposition 7.1 when （7.6） holds
9. Removing the assumption （6.1）
10. The second alternative
11. The second alternative concluded
12. Proof of the main proposition
13. Boundary regularity
14. Miscellaneous remarks
15. Bibliographical notes
V. Boundedness of weak solutions
1. Introduction
2. Quasilinear parabolic equations
3. Sup-bounds
4. Homogeneous structures. The degenerate case 1 p > 2
5. Homogeneous structures. The singular case 1 2
l. Introduction
2. The intrinsic Hamack inequality
3. Local comparison functions
4. Proof of Theorem 2.1
5. Proof of Theorem 2.2
6. Global versus local estimates
7. Global Hamack estimates
8. Compactly supported initial data
9. Proof of Proposition 8.1
10. Proof of Proposition 8.1 continued
11. Proof of Proposition 8. i concluded
12. The Cauchy problem with compactly supported initial data
13. Bibliographical notes
VII. Hamack estimates and extinction profile for singular equations
1. The Harnack inequality
2. Extinction in finite time （bounded domains）
3. Extinction in finite time （in RN）
4. An integral Hamack inequality for all
5. Sup-estimates for
6. Local subsolution.
7. Time expansion of positivity
8. Space-time configurations
9. Proof of the Hamack inequality
10. Proof of Theorem 1.2
11. Bibliographical notes
VIII. Degenerate and singular parabolic systems
1. Introduction
2. Boundedness of weak solutions
3. Weak differentiability of Du and energy estimates for IOul
4. Boundedness of lOut. Qualitative estimates
5. Quantitative sup-bounds of
6. General structures
7. Bibliographical notes
IX. Parabolic p-systems： Hiolder continuity of Du
1. The main theorem
2. Estimating the oscillation of Du
3. Hlder continuity of Du （the case p > 2 ）
4. HOlder continuity of Du （the case 1 2）
5. Estimating the local average of IDwl （the case p > 2 ）
6. Estimating the local averages of w （the case p > 2 ）
7. Comparing w and v （the case max 1 2
1. Introduction
2. Behaviour of non-negative solutions as
3. Proof of （24）
4. Initial traces
……
Ⅻ Non-ngative solutions in tThe Case
Bibliography