Let $u:A\cup B\to R$ be a function (where $A$ and $B$ are disjoint connected sets and $A\cup B$ is connected) such that $u$ restrict to $A$ and to $B$ are in $W^{1, p}$. Which result guarantees me that $u$ is $W^{1, p}$?
How can we glue Sobolev functions?
2
$\begingroup$
functions
sobolev-spaces
-
0Thanks @bogus and Leonid for your remarks. – 2012-06-22