Timeline for Moser regularity proof avoiding John-Nirenberg lemma
Current License: CC BY-SA 3.0
6 events
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| May 13, 2012 at 23:34 | comment | added | Spencer | To clarify, the rest of Tilli's paper - i.e. the non-so-new stuff - looks, at a glance, to be the same as the old argument that's in Han and Lin. So it seems a perfectly good source. | |
| May 13, 2012 at 23:31 | comment | added | Spencer |
The new point about this paper Mircea seems to be that they avoid the iteration altogether, by basically differentiating' the quantity which is usually treated discretely and iterated. A proof along the lines which Connor describes in his initial answer, i.e. for pure divergence form equations, using iteration but not John-Nirenberg existed right at the start' as it were - it is due essentially to De Giorgi himself. You can find it the book of Han and Lin, Elliptic PDE. The John-Nirenberg Lemma was used by Moser to prove his Harnack inequality, which itself was not crucial for regularity.
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| Mar 26, 2012 at 15:20 | comment | added | Connor Mooney | I hadn't seen the paper before, but that's exactly the proof I was thinking of. Thanks for the reference! | |
| Mar 25, 2012 at 18:27 | comment | added | Mircea | ..was that what you were referring to? | |
| Mar 25, 2012 at 18:25 | comment | added | Mircea | Thank you, this is a nice proof indeed, it is due to P. Tilli, I think ("Remarks on the Hölder continuity of solutions to elliptic equations in divergence form",Calculus of Variations and Partial Differential Equations, Vol. 25, Number 3, 395-401, DOI: 10.1007/s00526-005-0348-3) | |
| Mar 25, 2012 at 18:07 | history | answered | Connor Mooney | CC BY-SA 3.0 |