
Differential Equations Ordinary and Partial Differential Equations Math Forum 
 LinkBack  Thread Tools  Display Modes 
October 9th, 2018, 08:04 AM  #1 
Senior Member Joined: Jan 2015 From: usa Posts: 104 Thanks: 1  A PDE solution
Let $f\in C^2(\mathbb{R}^n)$. We define $$\phi(x,r)=\frac{1}{n\alpha(n)}\int_{\partial B(0,1)}f(x+rz)dS(z)$$ where $\alpha(n)$ is the volume of $B(0,1)$. I calculated $$\partial_r\phi=\frac{r}{n\alpha(n)} \int_{\partial B(0,1)}\Delta_xf(x+rz)dS(z)$$ Please help me to show that $$\partial_{rr}\phi\frac{n1}{r}\partial_r\phi=\Delta_x\phi$$ Thanks. Last edited by skipjack; October 9th, 2018 at 12:52 PM. 
October 9th, 2018, 09:20 AM  #2  
Senior Member Joined: Jan 2015 From: usa Posts: 104 Thanks: 1 
This is the right version Quote:
Last edited by skipjack; October 9th, 2018 at 12:53 PM.  
October 9th, 2018, 10:18 AM  #3 
Senior Member Joined: Sep 2016 From: USA Posts: 555 Thanks: 319 Math Focus: Dynamical systems, analytic function theory, numerics 
Ahh so we have graduated from doing your abstract algebra HW to doing your PDE HW. It's nice to be promoted.
Last edited by skipjack; October 9th, 2018 at 12:53 PM. 
November 2nd, 2018, 10:11 AM  #4 
Banned Camp Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 124  

Tags 
pde, solution 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Why my solution is different from sample solution?  rain  Real Analysis  1  July 17th, 2013 01:28 PM 
solution for a^x + bx  c =0  niraj  Algebra  5  December 14th, 2012 08:27 AM 
my correct solution but another solution?  davedave  Calculus  1  January 31st, 2012 03:48 PM 
solution  bentick  Algebra  11  April 15th, 2010 12:15 AM 
trying to make a solution (liquid solution...) problem...  TreeTruffle  Algebra  2  March 27th, 2010 02:22 AM 