### 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.

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.

#### Keywords

Anisotropic elliptic equations; existence and regularity results; Mountain Pass Theorem; $L^1$ data

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