1-Extension of Sobolev functions over the real plane
$begingroup$
Let $Omega$ be the region ${(x,y) in mathbb{R}^2 | y >x^2}$. I would like to determine whether there exists a continuous extension map $$E:W^{1,p}(Omega) to W^{1,p}(mathbb{R}^2) .$$
Here we do not have the standard hypothesis to get such an extension like for example having $partialOmega$ compact,so I was trying to prove that it is false by invalidating some of the consequences this extension would imply, but I was not able to get any further
functional-analysis sobolev-spaces
asked Dec 29 '18 at 13:02
Tommaso ScognamiglioTommaso Scognamiglio
507312
$endgroup$
add a comment |
$begingroup$
Let $Omega$ be the region ${(x,y) in mathbb{R}^2 | y >x^2}$. I would like to determine whether there exists a continuous extension map $$E:W^{1,p}(Omega) to W^{1,p}(mathbb{R}^2) .$$
Here we do not have the standard hypothesis to get such an extension like for example having $partialOmega$ compact,so I was trying to prove that it is false by invalidating some of the consequences this extension would imply, but I was not able to get any further
functional-analysis sobolev-spaces
asked Dec 29 '18 at 13:02
Tommaso ScognamiglioTommaso Scognamiglio
507312
$endgroup$
add a comment |
$begingroup$
Let $Omega$ be the region ${(x,y) in mathbb{R}^2 | y >x^2}$. I would like to determine whether there exists a continuous extension map $$E:W^{1,p}(Omega) to W^{1,p}(mathbb{R}^2) .$$
Here we do not have the standard hypothesis to get such an extension like for example having $partialOmega$ compact,so I was trying to prove that it is false by invalidating some of the consequences this extension would imply, but I was not able to get any further
functional-analysis sobolev-spaces
asked Dec 29 '18 at 13:02
Tommaso ScognamiglioTommaso Scognamiglio
507312
$endgroup$
Let $Omega$ be the region ${(x,y) in mathbb{R}^2 | y >x^2}$. I would like to determine whether there exists a continuous extension map $$E:W^{1,p}(Omega) to W^{1,p}(mathbb{R}^2) .$$
Here we do not have the standard hypothesis to get such an extension like for example having $partialOmega$ compact,so I was trying to prove that it is false by invalidating some of the consequences this extension would imply, but I was not able to get any further
functional-analysis sobolev-spaces
functional-analysis sobolev-spaces
asked Dec 29 '18 at 13:02
Tommaso ScognamiglioTommaso Scognamiglio
507312
asked Dec 29 '18 at 13:02
Tommaso ScognamiglioTommaso Scognamiglio
507312
asked Dec 29 '18 at 13:02
Tommaso ScognamiglioTommaso Scognamiglio
507312
asked Dec 29 '18 at 13:02
Tommaso ScognamiglioTommaso Scognamiglio
507312
asked Dec 29 '18 at 13:02
Tommaso ScognamiglioTommaso Scognamiglio
507312
507312
add a comment |
add a comment |
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