  We study families of strongly elliptic, second order differential operators
with singular coefficients on domains with conical points. We obtain uniform
estimates on their inverses and on the regularity of the solutions to the
associated Poisson problem with mixed boundary conditions. The coefficients and
the solutions belong to (suitable) weighted Sobolev spaces. The space of
coefficients is a Banach space that contains, in particular, the space of
smooth functions. Hence, our results extend classical well-posedness results
for strongly elliptic equations in domains with conical points to problems with
singular coefficients. We furthermore provide precise uniform estimates on the
norms of the solution operators.
