Stanislas Ouaro

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We study well-posedness for elliptic problems under the form b(u) − div a(x, u,∇u) = f, where a satisfies the classical Leray-Lions assumptions with an exponent p that may depend both on the space variable x and on the unknown solution u. A prototype case is the equation u − div | ∇u| p(u)−2 ∇u = f. We have to assume that inf x∈Ω, z∈R p(x, z) is greater(More)
We study the structural stability (i.e., the continuous dependence on coefficients) of solutions of the elliptic problems under the form b(u n) − div a n (x,∇u n) = f n. The equation is set in a bounded domain Ω of R N and supplied with the homogeneous Dirichlet boundary condition on ∂Ω. Here b is a non-decreasing function on R, and a n (x, ξ) n is a family(More)
In this article we study the nonlinear homogeneous Neumann boundary-value problem b(u) − div a(x, ∇u) = f in Ω a(x, ∇u).η = 0 on ∂Ω, where Ω is a smooth bounded open domain in R N , N ≥ 3 and η the outer unit normal vector on ∂Ω. We prove the existence and uniqueness of a weak solution for f ∈ L ∞ (Ω) and the existence and uniqueness of an entropy solution(More)
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