  The goal of this paper is to study some possibly degenerate elliptic equation
in a bounded domain with a nonlinear boundary condition involving measure data.
We investigate two types of problems: the first one deals with the laplacian in
a bounded domain with measure supported on the domain and on the boundary. A
second one deals with the same type of data but involves a degenerate weight in
the equation. In both cases, the nonlinearity under consideration lies on the
boundary. For the first problem, we prove an optimal regularity result, whereas
for the second one the optimality is not guaranteed but we provide however
regularity estimates.
