𝐿∞-Solutions for Some Nonlinear Degenerate Elliptic Equations

Abstract

We are interested in the existence of solutions for Dirichlet problem associated to the degenerate quasilinear elliptic equations −∑𝑛𝑗=1𝐷𝑗[𝜔2(𝑥)𝒜𝑗(𝑥,𝑢,∇𝑢)]+𝜔1(𝑥)𝑔(𝑥,𝑢(𝑥))+𝐻(𝑥,𝑢,∇𝑢)𝜔2(𝑥)=𝑓(𝑥),onΩ in the setting of the weighted Sobolev spaces W01,𝑝(Ω,𝜔1,𝜔2).