Abstract
We are interested in the degenerate problem: b(v) −divA(v,∇g(v)) = f in Ω with the boundary condition v = a ,w herea : ∂Ω → 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, nondecreas- ing with lim r→±∞ |b+g|(r) < +∞ ,t hatg hat a flat region (A1,A2) and is strictly increasing on R \(A1,A2) for some A1 0 A2. Using monotonicity methods, we prove the existence and uniqueness of a renormalized entropy solution (with possibly infinite values).
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