Anisotropic elliptic equations in $mathbb R^{N}$: existence and regularity results

Abstract

We investigate a class of anisotropic elliptic equations in the whole $\mathbb R^N$. By a variational approach, we obtain existence and regularity of nontrivial solutions in the framework of anisotropic Sobolev spaces. In addition, when the data is assumed to be merely locally integrable, the existence of solutions is established for a subclass of equations.