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November/December 2012 On the equation $\det\nabla \varphi=f$ prescribing $\varphi=0$ on the boundary
Olivier Kneuss
Differential Integral Equations 25(11/12): 1037-1052 (November/December 2012). DOI: 10.57262/die/1356012250


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$.


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Olivier Kneuss. "On the equation $\det\nabla \varphi=f$ prescribing $\varphi=0$ on the boundary." Differential Integral Equations 25 (11/12) 1037 - 1052, November/December 2012.


Published: November/December 2012
First available in Project Euclid: 20 December 2012

zbMATH: 1274.35050
MathSciNet: MR3013403
Digital Object Identifier: 10.57262/die/1356012250

Primary: 35F30

Rights: Copyright © 2012 Khayyam Publishing, Inc.

Vol.25 • No. 11/12 • November/December 2012
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