Victor LAHNO 1 and Stanislav SPICHAK 2
1Poltava State Pedagogical University,
 2 Ostrogradskoho Str.,
 Poltava,
 UKRAINE
   and
2Institute of Mathematics of NAS of Ukraine,
 3 Tereshchenkivs'ka Str.,
 01601 Kyiv,
 UKRAINE
E-mail: laggo@poltava.bank.gov.ua, spichak@imath.kiev.ua

Preliminary group classification of general two-dimensional quasi-linear elliptic type equations

Abstract:
Group classification of two-dimensional quasi-linear elliptic type equations with an arbitrary function of arguments $x$, $y$, $u(x,y)$, $u_x$, $u_y$ is carried out under simple, two- and three-dimensional solvable algebras.