Timeline for Reverse Holder Inequality and the higher integrability of the gradient of a solution to Euler's equation for a certain functional
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 4, 2014 at 3:27 | comment | added | Nirav | @Kelei and @ Deane- I've just gone over my workings and you are right. Giaquinta's and Giusti's proof is valid for n=2. I'll look up Moser's iteration method anyhow...Thanks | |
| Jan 4, 2014 at 1:06 | history | edited | Nirav | CC BY-SA 3.0 |
deleted 2 characters in body
|
| Jan 3, 2014 at 16:23 | comment | added | Deane Yang | I don't know how Giaquinta and Giusti prove this, but I'm pretty sure it can be proved using Moser iteration (where you inductively prove $L^p$ bounds for an increasing sequence of $p$ (determined by the exponents involved in the Sobolev inequality) on a decreasing sequence of balls. The inductive step uses integration by parts, the Hölder inequality, and the Sobolev inequality. And, as Kelei says, I don't believe the sharp version of Sobolev is needed for for this. | |
| Jan 3, 2014 at 10:34 | comment | added | Kelei Wang | Does the argument need the Sobolev-Poincare with the Sobolev exponent $\frac{2n}{n-2}$? Perhaps any one between $2$ and this is sufficient. | |
| Jan 3, 2014 at 8:17 | review | First posts | |||
| Jan 3, 2014 at 8:54 | |||||
| Jan 3, 2014 at 8:01 | history | asked | Nirav | CC BY-SA 3.0 |