Timeline for A question about the $C^{2,\alpha}$ regularity of concave fully nonlinear uniformly elliptic equation
Current License: CC BY-SA 3.0
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| Jul 25, 2013 at 13:45 | comment | added | Connor Mooney | I've slightly modified the answer to make it clearer. A function whose second derivative has a Holder continuous modification is in fact $C^{2,\alpha}$, by producing a quadratic approximation at $x$ as a limit of those at nearby points. | |
| Jul 25, 2013 at 13:42 | history | edited | Connor Mooney | CC BY-SA 3.0 |
added 162 characters in body
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| Jul 25, 2013 at 11:38 | vote | accept | Thomas | ||
| Jul 25, 2013 at 11:13 | comment | added | Thomas | Thanks for your answer. I misunderstand your statement for the second problem. The essential diameter of $D^2u(B_{\delta^k}(x))$ is bounded above by the $C^{1,1}$ norm of $u$ in $B_1$. Is not the definition of essential diameter the diameter of $D^2u(B_{\delta^k}(x))$ up to a subset with measure zero? So my obstruction is we can allow the discontinuity of $D^2u$ for a subset with measure zero by the definition of essential diameter. Maybe I misunderstand the definition of essential diameter. | |
| Jul 25, 2013 at 7:24 | history | answered | Connor Mooney | CC BY-SA 3.0 |