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Arnold's Trivium
1991 Arnold's Trivium
68
Problem 68
Problem 68
Source:
July 1, 2010
Problem Statement
Find
inf
∬
x
2
+
y
2
≤
1
(
∂
u
∂
x
)
2
+
(
∂
u
∂
y
)
2
d
x
d
y
\inf\iint_{x^2+y^2\le1}\left(\frac{\partial u}{\partial x}\right)^2+\left(\frac{\partial u}{\partial y}\right)^2dxdy
in
f
∬
x
2
+
y
2
≤
1
(
∂
x
∂
u
)
2
+
(
∂
y
∂
u
)
2
d
x
d
y
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