Abstract
We are interested in the degenerate problem: b(v) - divA(v,del g(v)) = f in Omega with the boundary condition v = a, where a : partial derivative Omega -> R is measurable such that g(a) = 0. We suppose that the vector field A satisfies the Leray-Lions conditions, that b, g are continuous, nondecreasing with (SIC) |b + g|(r) < +infinity, that g hat a flat region [A(1), A(2)] and is strictly increasing on R \ [A(1), A(2)] for some A(1) <= 0 <= A(2). Using monotonicity methods, we prove the existence and uniqueness of a renormalized entropy solution (with possibly infinite values).