I am trying to show that if $\varphi \in C^{\infty}(\partial M)$ then there is $\psi \in C^{\infty}(M)$ with $\psi|_{\partial M}=\varphi$ e $\Delta \psi=0$, where $M$ is a compact riemannian manifold with boundary and $\Delta: C^{\infty}(M)\rightarrow C^{\infty}(M)$ is the laplacian.

Thanks for your help.


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