We investigate the well-posedness of the classical Lifshitz-Slyozov-Wagner mean-field model for Ostwald ripening with singular coefficients, as they appear, for example in two-dimensional diffusion controlled growth. For Hölder-continuous initial data we prove the existence and uniqueness of a global solution with bounded mean-field. If the data are only in
L
l
o
c
q
(
[
0
,
∞
)
)
L^q_{loc}([0,\infty ))
for some
q
>
1
q>1
we establish global existence of a solution with a mean-field that is in general unbounded but in
L
r
(
0
,
T
)
L^r(0,T)
for some
r
>
1
r>1
that depends on the coefficients in the model.