I've been asked to compute the fundamental solution (in the distributional case) of the Laplacian. I have reach $u(r)=c\cdot r+c'$ for $r>0$ but i don't know how to prove that $\Delta u=\delta_0$, any hint?
Laplace equation
1
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functional-analysis
pde
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1In dimension $1$, you have to check that $\int_{\Bbb R}(cr+c')\phi''(r)dr=\phi(0)$ for all $\phi$ smooth with compact support. – 2012-12-08
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0ok, I think at the end you get $c=\frac{1}{2}$ right? – 2012-12-08
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0I haven't done the computation. Maybe you can write it in an answer. – 2012-12-08