2,638 reputation
1516
bio website stefuzius.wordpress.com
location
age
visits member for 2 years, 1 month
seen 7 hours ago

stefuzius84 (at) web (dot) de


7h
accepted Properties of the Double Layer Potential
7h
asked Show that Fourier series arising in solution of differential eqn. converges uniformly
7h
comment Properties of the Double Layer Potential
I come from the inside, so it equals $4\pi \nu_0$, right?
7h
comment Properties of the Double Layer Potential
Yes, okay, there comes a minus sign! :) Okay, and for b), is $W_{\nu}^i(x) = 0$?
7h
comment Properties of the Double Layer Potential
In your last comment it should be $2(x-y)$ not $2(y-x)$? And regarding part b), is $W_{\nu}^i(x) = 0$?
8h
comment Properties of the Double Layer Potential
Yes, regarding the surface element, I saw it just in the moment your comment came, so this is clear to me now :) But then it is still wrong up to a minus sign, or you forgot the minus sign in your post I guess... and also what about part b)... do you have mentioned it?
8h
comment Properties of the Double Layer Potential
I am not sure about $$ \int_{\partial B_{\varepsilon}(x)} \nabla_y \frac{1}{|x-y|} \cdot d\overline{S}(y) = 4\pi $$ we have $$ \nabla_y \frac{1}{|x-y|} = -\frac{1}{|x-y|^3} \cdot (x-y)$$ and the (inward pointing normal) is $$ \frac{x-y}{|x-y|} $$ so that this integral becomes $$\int_{\partial B_{\varepsilon}(x)} \frac{-1}{|x-y|^2} dx = \int_{\partial B_{\varepsilon}(x)} \frac{-1}{\varepsilon^2} dx = -\frac{4\pi}{\varepsilon}?$$ Which is differenent from your result?
9h
comment Properties of the Double Layer Potential
where do you need that $x \notin \Omega$ for part a)?
1d
asked Properties of the Double Layer Potential
Jul
22
accepted Conceptual Question on different representations of Hyperplanes, Higher Standpoint, Coordinate-free
Jul
18
accepted The Dirac Delta Distribution $\delta_0 : D \to \mathbb R$ is not regular
Jul
18
revised The Dirac Delta Distribution $\delta_0 : D \to \mathbb R$ is not regular
added 18 characters in body
Jul
18
asked The Dirac Delta Distribution $\delta_0 : D \to \mathbb R$ is not regular
Jul
18
comment Conceptual Question on different representations of Hyperplanes, Higher Standpoint, Coordinate-free
Yes of course, actually I meant solvable for any variable, not necessarily the last.
Jul
17
asked Conceptual Question on different representations of Hyperplanes, Higher Standpoint, Coordinate-free
Jul
17
accepted $\lim_{x\to 0+}\ln(x)\cdot x = 0$ by boundedness of $\ln(x)\cdot x$
Jul
16
comment $\lim_{x\to 0+}\ln(x)\cdot x = 0$ by boundedness of $\ln(x)\cdot x$
it is from here, what cow_gone_mad wrote, but it is in german... matheplanet.com/…
Jul
16
comment $\lim_{x\to 0+}\ln(x)\cdot x = 0$ by boundedness of $\ln(x)\cdot x$
indeed it says exactly this, but then it might be an error.
Jul
16
asked $\lim_{x\to 0+}\ln(x)\cdot x = 0$ by boundedness of $\ln(x)\cdot x$
Jul
16
accepted Rewriting integrals over spheres involving $1/|x|$