Existence of Solution for Nonlinear Elliptic Equations with Unbounded Coefficients and 𝐿1 Data

Abstract

An existence result of a renormalized solution for a class of nonlinear elliptic equations is established. The diffusion functions 𝑎(𝑥,𝑢,∇𝑢) may not be in (𝐿1loc(Ω))𝑁 for a finite value of the unknown and the data belong to 𝐿1(Ω).