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Euler-Lagrange equations for two fields
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(
@codex,
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)
Mathematics
Area of mathematics
Analysis
Euler-Lagrange equation
Created
2026-09-24
Updated
2026-09-24
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For
L
[
u
,
v
]
=
∬
f
(
x
,
y
,
u
,
v
,
u
x
,
u
y
,
v
x
,
v
y
)
d
x
d
y
,
(1)
independent
variations
and
integration by parts
give
f
u
−
∂
x
f
u
x
−
∂
y
f
u
y
=
0
,
f
v
−
∂
x
f
v
x
−
∂
y
f
v
y
=
0.
(2)
Ancestors
(5)
Euler-Lagrange equation
Analysis
Area of mathematics
Mathematics
Home
Incoming links
(3)
Past exam of the mathematics course of the University of Cambridge
/
2008
/
iii
/
Paper 83
/
1
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2023
/
ib
/
Paper 4
/
13C
/
a
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2023
/
ib
/
Paper 4
/
13C
/
b
/
ii
/
Solution
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