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

Mostafa Bendahmane, Said El Manouni

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.

Keywords


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

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