Abstract
We investigate a nonlinear elliptic Dirichlet problem with growth in fully anisotropic and non-reflexive Orlicz-Sobolev space. We do not impose any condition of doubling type. When the datum is regular, we prove existence of weak solutions. For measure data we consider a generalized notion of solutions for which we infer existence and anisotropic regularity in Orlicz-Marcinkiewicz spaces extending the known results for anisotropic p-Laplace equation. In the case of merely integrable data we prove also uniqueness. The regularity we infer in particular extends what is known for anisotropic p-Laplace equation.
