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Arnold's Trivium
1991 Arnold's Trivium
67
Problem 67
Problem 67
Source:
July 1, 2010
Problem Statement
What is the dimension of the space of solutions continuous on
x
2
+
y
2
≥
1
x^2+y^2\ge1
x
2
+
y
2
≥
1
of the problem
Δ
u
=
0
for
x
2
+
y
2
>
1
\Delta u=0\text{ for }x^2+y^2>1
Δ
u
=
0
for
x
2
+
y
2
>
1
∂
u
/
∂
n
=
0
for
x
2
+
y
2
=
1
\partial u/\partial n=0\text{ for }x^2+y^2=1
∂
u
/
∂
n
=
0
for
x
2
+
y
2
=
1
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