  In this note we prove equicontinuity for the family of one-point densities
with respect to a two-dimensional Coulomb gas at an inverse temperature
$\beta\ge 1/2$ confined by an external potential of Hele-Shaw (or
quasi-harmonic) type. As a consequence, subsequential limiting Lipschitz
continuous densities are defined on the microscopic scale. There are several
additional results, for example comparing the one-point density with the
thermal equilibrium density.
