Differential and Integral Equations

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

Olivier Kneuss

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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

Permanent link to this document
https://projecteuclid.org/euclid.die/1356012250

Mathematical Reviews number (MathSciNet)
MR3013403

Zentralblatt MATH identifier
1274.35050

Subjects
Primary: 35F30: Boundary value problems for nonlinear first-order equations

Citation

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


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