Timeline for Moser iteration for elliptic systems
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
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| Oct 6, 2015 at 12:29 | comment | added | username | It is all about what definition you use for coercivity. Many problems are fine, of course, as they are just like the scalar ones, e.g. uniformly convex ones, diagonally dominant problems ... | |
| Mar 22, 2012 at 19:00 | comment | added | Mircea | I don't know how much you want to be precise in imitating the arguments, but if you admit some sloppiness, then you'll be in trouble finding anything not using those methods. There is the "small energy implies regularity" result for systems (as in the treatment Evans in the answer of Hung Tran below) where the excess decay is proved much like in De Giorgi's method. A bootstrap like Moser is instead present in the very influential paper by Uhlenbeck form 1977 (Regularity for a class of non-linear elliptic systems. Acta Math. 138 (1977), no. 3-4, 219–240.). | |
| Sep 15, 2010 at 18:11 | vote | accept | timur | ||
| Sep 15, 2010 at 17:24 | history | edited | Johannes Hahn | CC BY-SA 2.5 |
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| Sep 15, 2010 at 17:18 | comment | added | Johannes Hahn | You're right: There are cases where a De-Giorgi-type argument still works and this is currently an active field of research. I don't know a specific example. | |
| Sep 15, 2010 at 15:52 | comment | added | timur | Thanks a lot for your answer! It seems that one counterexample would not rule out the possibility that the argument can be applied to specific situations. Or this example just kills everything? Do you know a specific example where similar type of argument has been successfully applied? | |
| Sep 15, 2010 at 9:39 | history | answered | Johannes Hahn | CC BY-SA 2.5 |