Timeline for Density of $H^{1/2}(\partial \Omega)$ in $L_2(\partial\Omega)$
Current License: CC BY-SA 3.0
5 events
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| Apr 21, 2012 at 12:36 | comment | added | Pietro Majer | Also, a $k$-Lipschitz function $f$ on a subset $Y$ of a metric space $(X,d)$ has a cheap $k$-Lipschitz extension $$\tilde f(x):=\inf_{y\in Y} f(y)+kd(x,y)$$ | |
| Apr 21, 2012 at 9:18 | vote | accept | Mike | ||
| Apr 21, 2012 at 9:10 | comment | added | Piero D'Ancona | If $f$ is Lipschitz on $\Gamma$, use a partition of unity to work locally, then use a Lipschitz continuous local change of variables to straighten the boundary, and you are reduced to the case $\Gamma$ is $x _n=0$. If you have a Lipschitz function on $x _n=0$ it is trivial to extend it to a Lipschitz function on the whole space (just take $F(x',x_n)=f(x')$). | |
| Apr 21, 2012 at 8:28 | comment | added | Mike | Hi, so there exists an extension operator from the set of Lipschitz continuous functions on $\Gamma$ to $H^1(\Omega)$? | |
| Apr 20, 2012 at 23:06 | history | answered | Piero D'Ancona | CC BY-SA 3.0 |