Geography Reference
In-Depth Information
G
22
/G
11
+
,
G
11
/G
22
+
.
∈
R
∈
R
(15.26)
Here, we are interested in a local solution of the ellipsoidal Korn-Lichtenstein equations around a
point
such that the relations
L
=
L
0
+
l
and
B
=
B
0
+
b
hold. A polynomial setup of the
local solution of the ellipsoidal Korn-Lichtenstein equations subject to the ellipsoidal vectorial
Laplace-Beltrami equations,
y
l
=
−
G
11
/G
22
x
b
,
b
=
G
22
/G
11
x
l
,
{
L
0
,B
0
}
(15.27)
G
22
/G
11
x
l
l
+
G
11
/G
22
x
b
b
=0
,
(15.28)
G
22
/G
11
y
l
l
+
G
11
/G
22
y
b
b
=0
,
is
x
(
l,b
)=
x
0
+
x
10
l
+
x
01
b
+
x
20
l
2
+
x
11
lb
+
x
02
b
2
+
x
30
l
3
+
x
21
l
2
b
+
x
12
lb
2
+
x
03
b
3
+
+O(4)
,
(15.29)
y
(
l, b
)=
y
0
+
y
10
l
+
y
01
b
+
y
20
l
2
+
y
11
lb
+
y
02
b
2
+
y
30
l
3
+
y
21
l
2
b
+
y
12
lb
2
+
y
03
b
3
+
+O(4)
,
or
x
(
l,b
)=
∞
P
n
(
l,b
)
,
n
=0
(15.30)
y
(
l,b
)=
∞
Q
n
(
l,b
)
,
n
=0
with
P
0
(
l,b
):=
x
0
,
P
1
(
l,b
):=
x
10
l
+
x
01
b
=
α
+
β
=1
x
αβ
l
α
b
β
,
P
2
(
l,b
):=
x
20
l
2
+
x
11
lb
+
x
02
b
2
=
α
+
β
=2
x
αβ
l
α
b
β
,
(15.31)
.
P
n
(
l,b
):=
α
+
β
=
n
x
αβ
l
α
b
β
,
and
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