Timeline for Reference request: importance of Lipschitz continuity
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 28, 2021 at 21:44 | answer | added | Dirk | timeline score: 4 | |
| Dec 28, 2021 at 21:22 | answer | added | Shannon Starr | timeline score: 3 | |
| Dec 28, 2021 at 20:44 | answer | added | Daniele Tampieri | timeline score: 2 | |
| Dec 24, 2021 at 10:52 | comment | added | Dave L Renfro | R.e. my last comment, this analogy may help. It can be useful to know the values of a (real-valued) function are bounded, and in many such cases (e.g. establishing error bounds for expressions containing the function) assuming the function is nice in some way so as to imply this (such as continuity on a compact set, or more generally the function has a uniformly bounded limit at each point such as this function) is an additional condition that is both unnecessary and somewhat obscures what really matters (boundedness of function values). | |
| Dec 24, 2021 at 3:42 | vote | accept | 12345 | ||
| Dec 24, 2021 at 0:41 | answer | added | WeakLearner | timeline score: 7 | |
| Dec 23, 2021 at 19:28 | comment | added | Dave L Renfro | It's probably worth observing that Lipschitz continuity is equivalent to having bounded rates of change, without the presumably (for these applications) unnecessary additional condition that all the pointwise limits of these rates of change actually exist. | |
| Dec 23, 2021 at 16:42 | comment | added | Pietro Majer | In general, talking of non-linear functional analysis in Banach spaces, just note that a Banach space may fail to have non-zero $C^1$ functions with bounded support. This means, no $C^1$ partitions of unity. On the other hand, locally Lipschits partitions of unity are available for free by means of the norm. So it is a lucky coincidence that the best regularity always available to build maps and vector fields is also the minimum requirement for well posedness of ODE. | |
| Dec 23, 2021 at 16:00 | answer | added | Iosif Pinelis | timeline score: 3 | |
| Dec 23, 2021 at 14:17 | history | edited | 12345 | CC BY-SA 4.0 |
added 151 characters in body; edited tags
|
| Dec 23, 2021 at 14:17 | review | Close votes | |||
| Jan 7, 2022 at 3:04 | |||||
| S Dec 23, 2021 at 13:58 | review | First questions | |||
| Dec 23, 2021 at 14:00 | |||||
| S Dec 23, 2021 at 13:58 | history | asked | 12345 | CC BY-SA 4.0 |