  The Special Lagrangian Potential Equation for a function $u$ on a domain
$\Omega\subset {\bf R}^n$ is given by ${\rm tr}\{\arctan(D^2 \,u) \} = \theta$
for a contant $\theta \in (-n {\pi\over 2}, n {\pi\over 2})$. For $C^2$
solutions the graph of $Du$ in $\Omega\times {\bf R}^n$ is a special Lagrangian
submanfold. Much has been understood about the Dirichlet problem for this
equation, but the existence result relies on explicitly computing the
associated boundary conditions (or, otherwise said, computing the
pseudo-convexity for the associated potential theory). This is done in this
paper, and the answer is interesting. The result carries over to many related
equations -- for example, those obtained by taking $\sum_k \arctan\,
\lambda_k^{{\mathfrak g}} = \theta$ where ${{\mathfrak g}} : {\rm Sym}^2({\bf
R}^n)\to {\bf R}$ is a Garding-Dirichlet polynomial which is hyperbolic with
respect to the identity. A particular example of this is the deformed
Hermitian-Yang-Mills equation which appears in mirror symmetry. Another example
is $\sum_j \arctan \kappa_j = \theta$ where $\kappa_1, ... , \kappa_n$ are the
principal curvatures of the graph of $u$ in $\Omega\times {\bf R}$.
  We also discuss the inhomogeneous Dirichlet Problem ${\rm tr}\{\arctan(D^2_x
\,u)\} = \psi(x)$ where $\psi : \overline{\Omega}\to (-n {\pi\over 2}, n
{\pi\over 2})$. This equation has the feature that the pull-back of $\psi$ to
the Lagrangian submanifold $L\equiv {\rm graph}(Du)$ is the phase function
$\theta$ of the tangent spaces of $L$. On $L$ it satisfies the equation $\nabla
\psi = -JH$ where $H$ is the mean curvature vector field of $L$.
