Suppose that partial derivatives
are again partially differentiable with respect to
. Then
Evaluation |
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If is the class
on
, then
.
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If a function is the class ![]() |
SOLUTION
,
,
,
Class ![]() |
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SOLUTION To show
, we first evaluate these values.
SOLUTION
.
Laplace Equation |
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SOLUTION
Let
. Then
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SOLUTION 1.
. Thus,
2.
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When we express
by
. Then
is called Laplaian and the class
function
satisfying the equation
is called harmonic function.
Exercise4-15-2. |
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SOLUTION 1.
,
,
,
.
Thus,
2.
.
Thus,