Entropy solutions for a doubly nonlinear elliptic problem with variable exponent

AbstractWe study the boundary value problem b(u)−diva(x,∇u)=f in Ω, u=0 on ∂Ω, where Ω is a smooth bounded domain in RN (N⩾3) and diva(x,∇u) is a p(x)-Laplace type operator with p(.):Ω→[1,+∞) a measurable function and b a continuous and nondecreasing function from R→R. We prove the existence and uniqueness of an entropy solution for L1-data f