Timeline for Harmonic Functions

9 events

when toggle format	what		by	license	comment
Nov 26, 2012 at 5:30	vote	accept	Mykie
Nov 26, 2012 at 5:30
Jun 10, 2010 at 16:14	history	edited	Andrey Rekalo	CC BY-SA 2.5	added 538 characters in body; added 20 characters in body
Jun 10, 2010 at 14:47	comment	added	BS.		Your argument shows the result holds for any distributional $f$ (for instance a locally integrable $f$).
Jun 10, 2010 at 2:49	comment	added	Andrey Rekalo		Yes, it's a good analogy.
Jun 10, 2010 at 2:16	comment	added	Will Jagy		Excellent. Similar to the distinction between, say, Lipschitz and locally Lipschitz properties.
Jun 10, 2010 at 1:59	comment	added	Andrey Rekalo		Will, if we can choose however small but the same $\delta>0$ for every $(x_0,y_0)\in {\rm supp} g$, then we may write the Taylor expansion and safely pass to the limit in the integral. In your example, the upper bound on $\delta$ goes to $0$ when $y_0\to 0$. And the limiting function is discontinuous precisely on the line $y_0=0$.
Jun 10, 2010 at 1:35	comment	added	Andrey Rekalo		Will, I'm not sure the proof will work if the upper bound does not remain $>\epsilon>0$ for every $(x,y)$ in the support of $g$. The question is whether the passage to the limit $\delta\to 0$ in the integral can be justified in this case?
Jun 9, 2010 at 20:24	history	edited	Andrey Rekalo	CC BY-SA 2.5	deleted 10 characters in body
Jun 9, 2010 at 20:17	history	answered	Andrey Rekalo	CC BY-SA 2.5