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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 $W^{1, p}$?

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    Thanks @bogus and Leonid for your remarks.2012-06-22

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