estimates for the operator

Description

Niveau: Supérieur, Doctorat, Bac+8
Contents 1 L 2 estimates for the -operator 7 1.1 Hermitian ve tor bundles . . . . . . . . . . . . . . . . . . . . 7 1.2 L 2 theory on omplete manifolds . . . . . . . . . . . . . . . . 12 1.3 General estimates for . . . . . . . . . . . . . . . . . . . . . 17 1.4 on weakly pseudo onvex manifolds . . . . . . . . . . . . . . 19 2 Ellipti operators 25 2.1 The Sobolev spa es . . . . . . . . . . . . . . . . . . . . . . . . 25 2.2 A regularity theorem for ellipti operators . . . . . . . . . . . 27 3 The pseudo onvex ase 33 3.1 Pseudo onvex domains in Kahler manifolds . . . . . . . . . . 33 3.2 The L 2 estimates . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.3 The -problem with exa t support . . . . . . . . . . . . . . . 38 3.4 The -equation for extensible urrents .

• ewise smooth


• cau hy-riemann


• nm has


• dimensional stein


• smooth forms


• pseudo onvex


• duality argument

Informations

• Publié par: profil-zyak-2012
• Nombre de lectures: 6
• Langue: English

Extrait

of
Con
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ten
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1
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L
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2
of
estimates
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for
Sob
the
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2
-op
with
erator
h
7
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1.1
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Hermitian
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v
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ector

bundles
unit
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of
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R
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R
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5.4
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function
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7
metrics
1.2
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L
51
2
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theory
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on
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4.4
manifolds
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5
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The
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to
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81
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12
86
1.3
A.1
General
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estimates
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for
Im


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A.4
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4.2
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family
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The
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17
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1.4


supp
on
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w
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eakly
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pseudo
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to
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71
ex
tial
manifolds

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5.2
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eakly
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ex
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5.3
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at
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ersurfaces
19
signature
2
.
Elliptic
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op
.
erators
Examples
25
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2.1
.
The
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Sob
.
olev
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spaces
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Some
.
analysis
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regularized
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89
.
eddings
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spaces
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domains
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A.3
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partition
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25
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2.2
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A
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regularit
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y
1
theorem
Construction
for
a
elliptic
of
op
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erators
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4.3
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L
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estimates
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27
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3
.
The
.
pseudo
.

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v
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ex
.

.
33
.
3.1
.
Pseudo
61

The
v
-equation
ex
exact
domains
ort
in
.
K
.
ahler
.
manifolds
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.
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.
67
.
Applications
.
C
.
manifolds
.
5.1
.
tangen
.
Cauc
33
y-Riemann
3.2
.
The
.
L
.
2
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estimates
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71
.
Boundaries
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w
.
pseudo
.
v
.
domains
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74
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Applications
.
Levi
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C
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manifolds
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78
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Hyp
.
with
.
t
35
.
3.3
.
The
.

.
-problem
.
with
.
exact
.
supp
5.5
ort
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A
38
results
3.4
real
The
89

A
-equation

for
.
extensible
.

.
ts
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A.2
.
b
.
of
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olev
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on
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hitz
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.
43
.
4
92
The
A
w
function
eakly
.
q
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-con
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v
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ex
.

.
47
.
4.1
.

.
prop
.
erties
.
of
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w
93
eakly
A
q
of
-con
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domains
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94
.
47X
In
0
tro
H

!
In
1).
this
;
thesis,
y
w
℄
e
(
study
)
the

p;q
-problem
is
with

exact
X
supp
as
ort
X
in
regularit

2
do-
k
mains
)
with

Levi-degenerate
is
b
=
oundaries.
p;n
This
if
is
lo
the
The
follo

wing
of
problem:
and
Consider
ernel
a
;

the
manifold
alen
X
X
and
)
a
(
relativ

ely
f

;
domain
p;q

\

p;q
X
))
.
wing:
Let

f

2
n
C

1
d.
p;q
Stein
(
,
X
the
)

\
if
Ker
ositiv

T
b
e
e
a
a

smo
piecewise
oth
℄

the
-closed
H
(
H
p;
=
q
exact
)-form
in
on
the
X
the

bidegree
h
b
that
f
supp
k
f
;

supp

g
(in
N
other
1g
w
(
ords,
;
f
C
v
X
anishes
E
to

innite
C
order
(
at
;
the
Our
b
the
oundary
1
of
X

).
E
W
for
e

w
q
an
and
t
X
to
E
nd
ar
a
or
smo
is
oth
then
(

p;
h
q
Stein,
1)
Æ
form
exit
u
[El
on
is
X
X
satisfying
has
(


that
)
;
p;q
p

the

(see
u
[El],
=

f
C
supp

u
oth

in

some
W
d.
e
hand,
will

giv
(
e
)
some
1
p
E
ositiv
then
e
-problem
answ
p
ers
)
to
is
the
to
problem
-equation
(
up

oundary
)

p;q
p;
for
equation
t
discussed
w
=
o
f
dieren
C
t
p;q
t
X
yp
E
es
j
of
f
domains.

The
;
rst
2
t
[
yp
+
e
;
will
p;q
b
X
e

a
E
domain
=
satisfying
1
a
(

;
pseudo
;

)
v
Ker
exit
=
y
(

1
dition,
1
whic
X
h

w
E
e
:

result
"log
then
Æ
follo
-pseudo
Theorem

H
v
(
exit
;
y".
;
More
)
precisely
0
,
0
let
p
(
n;
X

;

!
1
)
H
b
(
e
;
an
;
n
)
-dimensional
sep
K
ate
ahler
F
manifold
example,
and
X

a

manifold,
X
an
a

domain.
X
Let
whic
Æ
is
b

e
satises
the
log
b
-pseudo
oundary
v

y
function
(see
of
℄

same
with
true
resp
(
ect
;
to
)
!
p
.
e
W

e
ature,
assume
is
that
1

0
has
is

ositiv
hitz
in
b
sense
oundary
Griths
and
[T
is
℄
log
[Su
Æ
The
-pseudo
where


v
n
ex,

that
is
is
smo

w

settled
(
[Mi/Sh
log
using
Æ
k
+
metho
h
On
)
other

if
C
is
!
and
for
p;q
some
X
C
E
>
=
0
p;q
and
(
some
;
b
)
ounded
0,
function
solving
h

on
with

.
sup-
Let
ort
E

!
p;q
X

b
equiv
e
t
a
solving


v
with
ector
y
bundle
to
and
b
set
in
C
n
k
in
p;q
(
(
q
X
This
;
has

een
;
2
Estatemen
INTR
anishes
ODUCTION
the
3
yield
in
then
[He/Io
Finally
℄

under
w
the
pseudo
same
order
assumption
(
on
,

.
theorem
If
p

oth
has
W
smo
et