## Differential and Integral Equations

### On the equation $\det\nabla \varphi=f$ prescribing $\varphi=0$ on the boundary

Olivier Kneuss

#### Abstract

We discuss the existence of a regular map $\varphi$ satisfying $$\left\{ \begin{array}{cl} \det\nabla \varphi=f & \text{in \Omega}\\ \varphi=0 & \text{on \partial \Omega,} \end{array} \right.$$ where $\Omega$ is a bounded smooth domain and $f$ is a regular function satisfying $\int_{\Omega}f=0$.

#### Article information

Source
Differential Integral Equations, Volume 25, Number 11/12 (2012), 1037-1052.

Dates
First available in Project Euclid: 20 December 2012

Kneuss, Olivier. On the equation $\det\nabla \varphi=f$ prescribing $\varphi=0$ on the boundary. Differential Integral Equations 25 (2012), no. 11/12, 1037--1052. https://projecteuclid.org/euclid.die/1356012250