The explicit general solution of trivial Monge-Ampère equation
type: Item
instance of: scholarly article
title: The explicit general solution of trivial Monge-Ampère equation
zbMATH Open document ID: 0948.35026
author: Vitaly Ushakov
published in: Commentarii Mathematici Helvetici
publication date: 2000-06-05T00:00:00Z
review text: Summary: The general solution of the equation \(z_{xx}z_{yy}-z^2_{xy}=0\) with minimal smoothness requirements is presented in explicit form; it depends on two functions of one variable. In particular, it allows to describe explicitly all developable surfaces (without planar points) in \(\mathbb{R}^3\). The domain and singularities of the solution are investigated.
Mathematics Subject Classification ID: 35G20
Mathematics Subject Classification ID: 53A05
Mathematics Subject Classification ID: 35A10
Mathematics Subject Classification ID: 35A20
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 35C05
zbMATH DE Number: 1455391
zbMATH Keywords: developable surfaces
MaRDI profile type: Publication
full work available at URL: s000140050115
OpenAlex ID: W2036561590
DOI: 10.1007/S000140050115
description: scientific article; zbMATH DE number 1455391