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Arnold's Trivium
1991 Arnold's Trivium
58
Problem 58
Problem 58
Source:
July 1, 2010
Problem Statement
Find the dimension of the solution space of the problem
∂
u
/
∂
z
‾
=
a
δ
(
z
—
−
i
)
+
b
δ
(
z
+
i
)
\partial u/\partial\overline{z} = a\delta(z —-i) + b\delta(z + i)
∂
u
/
∂
z
=
a
δ
(
z
—
−
i
)
+
b
δ
(
z
+
i
)
for
∣
z
∣
≤
2
|z|\le 2
∣
z
∣
≤
2
,
Im
u
=
0
\text{Im } u = 0
Im
u
=
0
for
∣
z
∣
=
2
|z| = 2
∣
z
∣
=
2
.
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