退化抛物方程

所属分类:数学  
出版时间:2010-1   出版时间:世界图书出版公司   作者:德贝内代托   页数:387  
Tag标签:微分方程  

内容概要

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。

书籍目录

Preface1.
Elliptic
equations:
Harnack
estimates
and
Holder
continuity
...2.
Parabolic
equations:
Hamack
estimates
and
holder
continuity
..3.
Parabolic
equations
and
systems4.
Main
resultsI.
Notation
and
function
spaces1.
Some
notation2.
Basic
facts
about3.
Parabolic
spaces
and
embeddings4.
Auxiliary
lemmas5.
Bibliographical
notesII.
Weak
solutions
and
local
energy
estimates1.
Quasilinear
degenerate
or
singular
equations2.
Boundary
value
problems3.
Local
integral
inequalities4.
Energy
estimates
near
the
boundary5.
Restricted
structures:
the
levels
k
and
the
constant
76.
Bibliographical
notesIII.
Holder
continuity
of
solutions
of
degenerate
parabolic
equations1.
The
regularity
theorem2.
Preliminaries3.
The
main
proposition4.
The
first
alternative5.
The
first
alternative
continued6.
The
first
alternative
concluded7.
The
second
alternative8.
The
second
alternative
continued9.
The
second
alternative
concluded10.
Proof
of
Proposition
3.111.
Regularity
up
to
t
=
012.
Regularity
up
to
ST.
Dirichlet
data13.
Regularity
at
ST.
Variational
data14.
Remarks
on
stability15.
Bibliographical
notesIV.
Holder
continuity
of
solutions
of
singular
parabolic
equations1.
Singular
equations
and
the
regularity
theorems2.
The
main
proposition3.
Preliminaries4.
Rescaled
iterations5.
The
first
alternative6.
Proof
of
Lemma
5.1.
Integral
inequalities7.
An
auxiliary
proposition8.
Proof
of
Proposition
7.1
when
(7.6)
holds9.
Removing
the
assumption
(6.1)10.
The
second
alternative11.
The
second
alternative
concluded12.
Proof
of
the
main
proposition13.
Boundary
regularity14.
Miscellaneous
remarks15.
Bibliographical
notesV.
Boundedness
of
weak
solutions1.
Introduction2.
Quasilinear
parabolic
equations3.
Sup-bounds4.
Homogeneous
structures.
The
degenerate
case
1
p
>
25.
Homogeneous
structures.
The
singular
case
1
<
p
<
26.
Energy
estimates7.
Local
iterative
inequalities8.
Local
iterative
inequalities9.
Global
iterative
inequalities10.
Homogeneous
structures
and
111.
Proof
of
Theorems
3.1
and
3.212.
Proof
of
Theorem
4.113.
Proof
of
Theorem
4.2..14.
Proof
of
Theorem
4.315.
Proof
of
Theorem
4.516.
Proof
of
Theorems
5.1
and
5.217.
Natural
growth
conditions18.
Bibliographical
notesVI.
Harnack
estimates:
the
case
p>2l.
Introduction2.
The
intrinsic
Hamack
inequality3.
Local
comparison
functions4.
Proof
of
Theorem
2.15.
Proof
of
Theorem
2.26.
Global
versus
local
estimates7.
Global
Hamack
estimates8.
Compactly
supported
initial
data9.
Proof
of
Proposition
8.110.
Proof
of
Proposition
8.1
continued11.
Proof
of
Proposition
8.
i
concluded12.
The
Cauchy
problem
with
compactly
supported
initial
data13.
Bibliographical
notesVII.
Hamack
estimates
and
extinction
profile
for
singular
equations1.
The
Harnack
inequality2.
Extinction
in
finite
time
(bounded
domains)3.
Extinction
in
finite
time
(in
RN)4.
An
integral
Hamack
inequality
for
all5.
Sup-estimates
for6.
Local
subsolution.7.
Time
expansion
of
positivity8.
Space-time
configurations9.
Proof
of
the
Hamack
inequality10.
Proof
of
Theorem
1.211.
Bibliographical
notesVIII.
Degenerate
and
singular
parabolic
systems1.
Introduction2.
Boundedness
of
weak
solutions3.
Weak
differentiability
of
Du
and
energy
estimates
for
IOul4.
Boundedness
of
lOut.
Qualitative
estimates5.
Quantitative
sup-bounds
of6.
General
structures7.
Bibliographical
notesIX.
Parabolic
p-systems:
Hiolder
continuity
of
Du1.
The
main
theorem2.
Estimating
the
oscillation
of
Du3.
Hlder
continuity
of
Du
(the
case
p
>
2
)4.
HOlder
continuity
of
Du
(the
case
1
<
p
<
2
)5.
Some
algebraic
Lemmas6.
Linear
parabolic
systems
with
constant
coefficients7.
The
perturbation
lemma8.
Proof
of
Proposition
l.1-(i)9.
Proof
of
Proposition
1.l-(ii)10.
Proof
of
Proposition
1.1-(iii)11.
Proof
of
Proposition
1.1
concluded12.
Proof
of
Proposition13.
Proof
of
Proposition
1.2
concluded14.
General
structures15.
Bibliographical
notesX.
Parabolic
p-systems:
boundary
regularity1.
Introduction2.
Flattening
the
boundary3.
An
iteration
lemma4.
Comparing
w
and
v
(the
case
p
>
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

图书封面

图书标签Tags

微分方程


    退化抛物方程下载



用户评论 (总计23条)

 
 

  •     听朋友说还挺好的!
  •     不错,用得上。
  •     内容还没看,可作为参考。
  •     课后习题感觉难,蛮不错的~
  •     不过跟一般的课本不一样,怎么没英文版的阿!!!
  •     计算数学专业必备,对于考研来说
  •     偏微分很蛋疼,不过总体偏基础。
  •     不错,要是有同步的习题答案就好了
  •     不是一般的常微分方程,可以!
  •     年前购买的,书都不错
  •     以后慢慢看,和教材一起买的
  •     还不错,要是价格再便宜些就好了!
  •     很必要,没啥好说的。。。
  •     不好,书本很小
  •     微分动力系统的经典教材,是本好事
  •     就是物流太不给力啦,可以搭配交大的书看。
  •     知识很全面,还可以
  •     亚马逊的书就是冲着靠谱来买的。,对我本人很有益!
  •     但书有点小啊,比较难
  •     也很便宜……不过这个版本有点低了,应该不错。书质量很好。
  •     堪称俄罗斯数学的顶梁之一,值得相关研究方向的读者仔细阅读
  •     恨不得骂译者,比较难读
  •     想在书上记点什么不太方便。,很好
 

自然科学类PDF下载,数学PDF下载。 PPT下载网 

PPT下载网 @ 2017