A question on existence of a Sobolev Hilbert space, where convergence implies uniform convergence
Clash Royale CLAN TAG#URR8PPP
up vote
0
down vote
favorite
Is there a Sobolev Hilbert space $H^k(Omega)$($Omega$ open subset of $mathbbR^m$, with a smooth boundary), for some $k in mathbbN$, such that, any sequence in the space $C^0(barOmega)cap H^k(Omega)$, that converges in the norm $|.|_H^k$, also has to converge in the norm $|.|_C^0(barOmega)$
real-analysis functional-analysis sobolev-spaces
asked Aug 15 at 5:59
Rajesh Dachiraju
1,43422664
add a comment |Â
up vote
0
down vote
favorite
Is there a Sobolev Hilbert space $H^k(Omega)$($Omega$ open subset of $mathbbR^m$, with a smooth boundary), for some $k in mathbbN$, such that, any sequence in the space $C^0(barOmega)cap H^k(Omega)$, that converges in the norm $|.|_H^k$, also has to converge in the norm $|.|_C^0(barOmega)$
real-analysis functional-analysis sobolev-spaces
asked Aug 15 at 5:59
Rajesh Dachiraju
1,43422664
3
Try to look up Sobolev's embedding theorem.
– gerw
Aug 15 at 6:50
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Is there a Sobolev Hilbert space $H^k(Omega)$($Omega$ open subset of $mathbbR^m$, with a smooth boundary), for some $k in mathbbN$, such that, any sequence in the space $C^0(barOmega)cap H^k(Omega)$, that converges in the norm $|.|_H^k$, also has to converge in the norm $|.|_C^0(barOmega)$
real-analysis functional-analysis sobolev-spaces
asked Aug 15 at 5:59
Rajesh Dachiraju
1,43422664
Is there a Sobolev Hilbert space $H^k(Omega)$($Omega$ open subset of $mathbbR^m$, with a smooth boundary), for some $k in mathbbN$, such that, any sequence in the space $C^0(barOmega)cap H^k(Omega)$, that converges in the norm $|.|_H^k$, also has to converge in the norm $|.|_C^0(barOmega)$
real-analysis functional-analysis sobolev-spaces
asked Aug 15 at 5:59
Rajesh Dachiraju
1,43422664
asked Aug 15 at 5:59
Rajesh Dachiraju
1,43422664
asked Aug 15 at 5:59
Rajesh Dachiraju
1,43422664
asked Aug 15 at 5:59
Rajesh Dachiraju
1,43422664
1,43422664
3
Try to look up Sobolev's embedding theorem.
– gerw
Aug 15 at 6:50
add a comment |Â
3
Try to look up Sobolev's embedding theorem.
– gerw
Aug 15 at 6:50
3
3
Try to look up Sobolev's embedding theorem.
– gerw
Aug 15 at 6:50
Try to look up Sobolev's embedding theorem.
– gerw
Aug 15 at 6:50
add a comment |Â
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2883247%2fa-question-on-existence-of-a-sobolev-hilbert-space-where-convergence-implies-un%23new-answer', 'question_page');
);
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
3
Try to look up Sobolev's embedding theorem.
– gerw
Aug 15 at 6:50