Second order regularity for the [formula omitted]-Laplace equations with [formula omitted] data on the right-hand side

Abstract

This work considers p(x)-Laplace equations involving the L2 function on the right-hand side. In particular, we extend classical W1,2 regularity estimates for the gradient of a solution to linear equations to nonlinear equations with variable exponents under minimal regularity assumptions on the boundary We focus on the global W1,2 estimate, which is motivated by the L2-coercivity results for quasilinear elliptic equations with Orlicz growth, as demonstrated in Cianchi and Maz’ya (2018).