  Suppose $M_{1}$ and $M_{2}$ are two special Lagrangian submanifolds of $\Rtn$
with boundary that intersect transversally at one point $p$. The set $M_{1}
\cup M_{2}$ is a singular special Lagrangian variety with an isolated
singularity at the point of intersection. Suppose further that the tangent
planes at the intersection satisfy an angle condition (which always holds in
dimension $n=3$). Then, $M_{1} \cup M_{2}$ is regularizable; in other words,
there exists a family of smooth, minimal Lagrangian submanifolds $M_{\alpha}$
with boundary that converges to $M_{1} \cup M_{2}$ in a suitable topology. This
result is obtained by first gluing a smooth neck into a neighbourhood of $M_{1}
\cap M_{2}$ and then by perturbing this approximate solution until it becomes
minimal and Lagrangian.
