JournalscmhVol. 75 , No. 1DOI 10.1007/s000140050115

The explicit general solution of trivial Monge-Ampère equation

  • V. Ushakov

    Elwood, Victoria, Australia
The explicit general solution of trivial Monge-Ampère equation cover

Abstract

The general solution of the equation zxxzyyzxy2=0z_{xx}z_{yy} - z_{xy}^2 = 0 with minimal smoothness requirements is presented in explicit form; it depends on 2 functions of one variable. In particular, it allows to describe explicitly all developable surfaces (without planar points) in R3\Bbb R^3 . The domain and singularities of the solution are investigated.