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APM346-2016F
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APM346--Lectures
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Chapter 8
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HA9, Problem6
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Topic: HA9, Problem6 (Read 2929 times)
Shentao YANG
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HA9, Problem6
«
on:
November 13, 2016, 01:20:23 PM »
Can any explain in detail the reason behind the hint "solution must be a harmonic polynomial of degree $3$ and it should depend only on $x^2+y^2+z^2$ and $z$"?
Concretely, there are $3$ question need to be addressed:
$(1)$ Why the solution need to be a harmonic polynomial?
$(2)$ Why it should have degree $3$?
$(3)$ Why it should depend only on $x^2+y^2+z^2$ and $z$ but not the other terms?
The solution from the previous year basically made no reasonable explanation and just copied words from the textbook
http://forum.math.toronto.edu/index.php?topic=731.0
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Victor Ivrii
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Re: HA9, Problem6
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Reply #1 on:
November 15, 2016, 07:06:04 AM »
Consider it as a Hint. We have not finished harmonic polynomials on the lecture.
Also, since problem depends only on $x^2+y^2$ and $z$ (is invariant with respect to rotations around $z$ axis), so does the solution
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Toronto Math Forum
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APM346-2016F
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APM346--Lectures
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Chapter 8
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HA9, Problem6