Existence and uniqueness of renormalized solutions to nonlinear elliptic equations with variable exponents and L1L1-data

We prove the existence and uniqueness of a renormalized solution to nonlinear elliptic equations with variable exponents and L1L1-data. The functional setting involves Sobolev spaces with variable exponents W1,p(⋅)(Ω)W1,p(⋅)(Ω).