Concepción García Vázquez

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

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 : (s0, + ∞) ↦ ℝ a continuous, strictly positive function which goes to infinity when s is near s0. On the other hand,

Sur un problème elliptique non linéaire avec diffusion singulière et second membre dans L1

\frac{A(x,s)}{\beta(s)}\in L^\infty(\Omega\times(s_0,+\infty))^{N\times N}

Modelos y sistemas dinámicos

. Also, the right-hand side f belongs to L1(Ω). We make use of the concept of renormalized solutions adapted to our problem.