Resumen de Local bounds, Harnack's inequality and Hölder continuity for divergence type elliptic equations with non-standard growth

Noemi Wolanski

• We obtain a Harnack type inequality for solutions to elliptic equations in divergence form with non-standard p(x)-type growth. A model equation is the inhomogeneous p(x)-Laplacian. Namely,Δp(x)u:=div(|∇u|p(x)−2∇u)=f(x)inΩ, for which we prove Harnack's inequality when f∈Lq0(Ω) if max{1,Np1}