Elliptic equations, multivalued xx-dependent graphs and Orlicz spaces

The paper concerns the system of equations −divσ(x)=−divF(x), (∇u(x),σ(x))∈A(x)(∇u(x),σ(x))∈A(x), where A(x)A(x) is a maximal, strictly monotone, xx-dependent multivalued graph with growth and coercivity conditions in Orlicz spaces. The existence of weak solutions is established by regularization via convolution and passage to the limit based on Young measures.