Regularity theory for a class of quasilinear equations

This paper addresses the analysis of the weak solution of − Δ p ω + ω = f in a bounded domain Ω subject to the boundary condition∂ ω ∂ ν = 0on ∂ Ω , when the data f belongs toL 2 ( Ω )and p > 2 . We prove existence and uniqueness of solution for this problem in the Nikolskii spaceN p ′ , 2 p / p ′( Ω ) . Moreover, we obtain energy estimates regarding the Nikolskii norm of ω in terms of theL 2 ( Ω )norm of f .