Group classification of quasilinear elliptic-type equations. I. Invariance with respect to Lie algebras with nontrivial Levi decomposition

Abstract

The problem of group classification of quasilinear elliptic-type equations in the two-dimensional space is considered. The list of all equations of this sort is obtained, which admit the semisimple Lie algebras of symmetry operators and the Lie algebras of symmetry operators with nontrivial Levi decomposition.