Abstract
We are interested in the degenerate problem b(v) - div a(v, del g(v)) - f
with the homogeneous boundary condition g(v) = 0 on some part of the boundary. The vector field a is supposed to satisfy the Leray-Lions conditions and the functions b, g to be continuous, nondecreasing and to verify the normalization condition b(0) = g(0) = 0 and the range condition R(b + g) = R. Using monotonicity methods, we prove existence and comparison results for renormalized entropy solutions in the L-1 setting.