on some anisotropic elliptic problem with measure data

We prove optimal existence results for entropy solutions to some anisotropic boundary value problems like { − ∑pn i=1 diai(x, w, ∇w) = f − div f(w) in ω, in ω, v = 0 on ∂ω, (0.1) where f ∈ l^1 (ω), f = (f1, ..., fn ) satisfies f ∈ (c 0 (r))n .and ω is a bounded, open subset of r n , n ≥ 2, and the function ai(x, s, ξ) verify the large monotonicity condition. the construction of the proof of our theorem is done by using minty’s lemma in its modified version.