Regular solutions for nonlinear elliptic equations, with convective terms, in Orlicz spaces

We establish some existence and regularity results to the Dirichlet problem, for a class of quasilinear elliptic equations involving a partial differential operator, depending on the gradient of the solution. Our results are formulated in the Orlicz–Sobolev spaces and under general growth conditions on the convection term. The sub- and supersolutions method is a key tool in the proof of the existence results.