Show Posts

This section allows you to view all posts made by this member. Note that you can only see posts made in areas you currently have access to.

Topics - Zacharie Leger

Pages: [1]
APM346--Misc / Final Marks on ROSI
« on: April 18, 2015, 12:38:55 AM »
Finial marks have been posted on ROSI!

HA9 / HA9 Problem 1
« on: March 24, 2015, 10:56:40 PM »
Find function $u$ harmonic in $\{x^2+y^2+z^2\le 1\}$ and coinciding with $g=z^4$ as $x^2+y^2+z^2=1$.

Hint. According to [Subsection 28.1] solution must be a harmonic polynomial of degree $4$ and it should depend only on $x^2+y^2+z^2$ and $z$ (Explain why). The only way to achive it (and still coincide with $g$ on $\{x^2+y^2+z^2=1\}$) is to find
u= z^4 + az^2(1-x^2-y^2-z^2)+b(1-x^2-y^2-z^2)^2
with unknown coefficients $a,b$.

It seems to me that we should have a harmonic polynomial of degree 4 if we want the function to coincide with $g(x)=z^4$ on ${x^2+y^2+z^2=1}$, I'm I missing something?

Pages: [1]