Timeline for Where to learn about parabolic Hölder spaces and when to use them
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| S Jul 21, 2015 at 21:28 | history | suggested | user71046 |
Added an extra tag appropriate to parabolic Holder spaces
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| Jul 21, 2015 at 20:27 | review | Suggested edits | |||
| S Jul 21, 2015 at 21:28 | |||||
| Jul 21, 2015 at 19:26 | answer | added | user71046 | timeline score: 4 | |
| Jul 7, 2012 at 20:31 | comment | added | user24394 | Thanks @Andrew. Very useful since my library doesn't stock Friedman unfortunately.. | |
| Jul 7, 2012 at 16:23 | comment | added | Andrew | @quentinknight a more recent book on Holder space theory in PDE is N. V. Krylov - Lectures on Elliptic and Parabolic Equations in Hölder Spaces books.google.com/… | |
| Jun 27, 2012 at 8:36 | comment | added | user24394 | Thanks for the responses. I'll look for that book in the library. | |
| Jun 26, 2012 at 16:41 | comment | added | Otis Chodosh | A widely used reference for parabolic PDE is Friedman's "PDE of Parabolic Type" which might be of some help. ams.org/mathscinet-getitem?mr=181836 | |
| Jun 26, 2012 at 16:10 | comment | added | YangMills | One simple reason why you get a payoff is the following "gain of derivatives" (let's consider the elliptic case, the parabolic case is similar): if $\Delta u=f$ in some domain and $f\in C^k$ it does not follow that $u\in C^{k+2}_{loc}$. However, if $f\in C^{k,\alpha}$ and $0<\alpha<1$, then it does follow that $u\in C^{k+2,\alpha}_{loc}$ by Schauder estimates. | |
| Jun 26, 2012 at 15:38 | comment | added | Willie Wong | Considering how much of PDE theory concerns finding suitable function spaces to use for a given equation, I doubt that there's any easy answer to "how do I know which function spaces to use" besides (a) experience (someone else used it and it worked) and (b) extreme cleverness (sadly, nothing that I am qualified to explain), plus a small dose of scaling considerations. | |
| Jun 26, 2012 at 15:06 | history | asked | user24394 | CC BY-SA 3.0 |