An Elliptic Equation with Blowing-Up Diffusion and Data in L¹: Existence and Uniqueness

Abstract

We establish some existence and uniqueness results for a nonlinear elliptic equation. The problem has a diffusion matrix A(x, u) such that A(x, s)ξξ ≥ β(s)|ξ| 2 , with β : (s 0 , + ∞) ↦ ℝ a continuous, strictly positive function which goes to infinity when s is near s 0 . On the other hand, [Formula: see text]. Also, the right-hand side f belongs to L 1 (Ω). We make use of the concept of renormalized solutions adapted to our problem.