Udrişte, C.; Bîlă, N. Symmetry Lie group of the Monge-Ampère equation. (English) Zbl 0934.58039 Balkan J. Geom. Appl. 3, No. 2, 121-134 (1998). The paper mainly deals with point symmetries of the Monge-Ampère equation \[ \det(\partial^2 u/\partial x^i \partial x^j) = f(x,u),\qquad 1 \leq i,\quad j \leq n. \] From the results: for \(n = 2\) and \(f = 1\), invariant solutions with respect to four optimal subalgebras are found, and a proof is given that among second-order equations the Monge-Ampère equation is uniquely determined by its symmetry algebra. For related earlier results also on contact symmetries see S. V. Khabirov [Math. USSR, Sb. 71, No. 2, 447-462 (1992); translation from Mat. Sb. 181, No. 12, 1607-1622 (1990; Zbl 0713.76085)]. [Reviewer’s remark: The same paper is reprinted in Appl. Sci. 1, No. 1, 60-73 (1999; Zbl 0934.58040)]. Reviewer: M.Marvan (Opava) Cited in 1 ReviewCited in 2 Documents MSC: 58J70 Invariance and symmetry properties for PDEs on manifolds 35A30 Geometric theory, characteristics, transformations in context of PDEs Keywords:infinitesimal symmetry; group-invariant solution; geometric dynamics; Monge-Ampère equation Citations:Zbl 0776.76079; Zbl 0713.76085; Zbl 0934.58040 PDFBibTeX XMLCite \textit{C. Udrişte} and \textit{N. Bîlă}, Balkan J. Geom. Appl. 3, No. 2, 121--134 (1998; Zbl 0934.58039) Full Text: EuDML EMIS