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Suppose we have the Boundary Value Problem (BVP):

$\Delta{u}=f$ , in the domain (topos) $D$

$\partial_{n}{u}=h$, in $\partial{D}$

It is easy to prove using $1$st Green's identity that a necessary condition for the above mentioned BVP is $\int_{\partial{D}}h=\int_{{D}}f$ . But how about the sufficient case here ? Is also this condition enough in order the BVP to have a solution. Any hint or ref is really appreciated.

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