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. We obtain the lists of all equations of this class that admit the semisimple Lie algebras of symmetry operators and the Lie algebras of symmetry operators with nontrivial Levi decomposition.