Timeline for Harmonic Functions
Current License: CC BY-SA 2.5
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 26, 2012 at 5:30 | vote | accept | Mykie | ||
| Jun 10, 2010 at 3:51 | comment | added | Will Jagy | Hi, Andrey. I had the feeling that such an example might be one of those axiom of choice things, but really elaborate even then. I certainly do not know how to construct it. All I can think of is constructing a non-measurable function by taking, on the real line, one representative for each equivalence class of the relation $x \sim y$ if and only if $x−y$ is rational. So wait, that trick shows that we can make a badly discontinuous example that works for all RATIONAL $\delta > 0.$ Points are equivalent if both $x$ and $y$ coordinates differ by rationals. Function constant on each class. | |
| Jun 10, 2010 at 2:58 | comment | added | Andrey Rekalo | It would be interesting to know if there is a discontinuous function $f$ which satisfies the discrete Laplace equation at every point and for every $\delta>0$. | |
| Jun 10, 2010 at 1:48 | history | edited | Will Jagy | CC BY-SA 2.5 |
my argument
|
| Jun 10, 2010 at 1:05 | history | edited | Will Jagy | CC BY-SA 2.5 |
absolute value of delta
|
| Jun 10, 2010 at 0:50 | history | edited | Will Jagy | CC BY-SA 2.5 |
local condition and discontinuity
|
| Jun 9, 2010 at 21:48 | vote | accept | Mykie | ||
| Nov 26, 2012 at 5:30 | |||||
| Jun 9, 2010 at 19:12 | history | edited | Will Jagy | CC BY-SA 2.5 |
deleted 49 characters in body
|
| Jun 9, 2010 at 18:54 | comment | added | Steven Gubkin | It is probably to late in the year for it to be homework. | |
| Jun 9, 2010 at 18:44 | history | answered | Will Jagy | CC BY-SA 2.5 |