We obtain existence and global regularity estimates for gradients of solutions
to quasilinear elliptic equations with measure data whose prototypes are of the form
in a bounded domain
potentially with nonsmooth
boundary. Here either
or
,
is a finite signed
Radon measure in
,
and
.
Our main concern is to extend earlier results to the strongly singular case
. In particular,
in the case
which corresponds to a Riccati-type equation, we settle the question of solvability
that has been raised for some time in the literature.
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