Timeline for Dependence of norm of extension map on Sobolev spaces and $(\epsilon,\delta)$ domains
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 21, 2011 at 22:01 | comment | added | Tapio Rajala | Averaging on spheres is equivalent to estimating by the radial direction. What argument comes after that can be chosen in many ways. I simply put one argument which I found to be the simplest to verify by one line of calculations. | |
| Jun 21, 2011 at 10:10 | vote | accept | Tom Leness | ||
| Jun 21, 2011 at 6:56 | comment | added | Andrew | The reasoning simplify somewhat if to take an extention (for constant function 1) which depends on $r$ only? Such an extention can be obtained from an arbitrary one by averaging on shperes. Put $r_0=1$, $r_1=1+\varepsilon$. By stretching arguments (to annulus $1<r<2$) there seems to exisit an extention $f$ with estimates $\|\partial ^l f\|_{L_p(\mathbb R^n)}\le C \varepsilon^{(n-l)/p}$, $|l|\le k$. So norms of some of the derivatives yet tends to zero then $\varepsilon\to+0$. | |
| Jun 20, 2011 at 12:48 | history | answered | Tapio Rajala | CC BY-SA 3.0 |