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Failure of the weak maximum principle with a positive zeroth-order coefficient
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Area of mathematics
Analysis
Partial differential equation
Elliptic boundary value problem
Uniformly elliptic operator
Weak maximum principle for elliptic operators
2026-10-03
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A
positive zeroth-order
coefficient
can destroy the weak
maximum principle
. On
(
0
,
1
)
, the
function
u
(
x
)
=
sin
(
π
x
)
has zero boundary values and
a
positive interior maximum, but
u
′′
+
π
2
u
=
0.
(1)
Ancestors
(8)
Weak maximum principle for elliptic operators
Uniformly elliptic operator
Elliptic boundary value problem
Partial differential equation
Analysis
Area of mathematics
Mathematics
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(2)
Past exam of the mathematics course of the University of Cambridge
/
2009
/
iii
/
Paper 12
/
1
/
iii
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2018
/
iii
/
Paper 107
/
2
/
a
/
Solution
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