Besov regularity estimates for the elliptic p(x)-Laplacian equation with the logarithmic growth

Abstract

In this paper we establish the local regularity estimates in Besov spaces of weak solutions for the elliptic p(x)-Laplacian equation with the logarithmic growth in divergence formdiv(|∇u|p(x)−2ln⁡(e+|∇u|)∇u)=divF under some proper assumptions on the functions p(x) and F. Moreover, it is worth noting that our results improve the known results for these types of equations.