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September  2014, 13(5): 1779-1787. doi: 10.3934/cpaa.2014.13.1779

Multiple Jacobian equations

Bernard Dacorogna 1, and  Olivier Kneuss 2,

1. 

Section de Mathématiques, Station 8, EPFL, 1015 Lausanne
2. 

Department of Mathematics, UC Berkeley, Berkeley, CA, 94720, United States

Received  July 2013 Revised  November 2013 Published  June 2014

The existence, regularity and uniqueness of a local diffeomorphism $\varphi$ satisfying \begin{eqnarray} g_{i}(\varphi) \det\nabla\varphi=f_{i}\quad for\ every\ 1\leq i\leq n \end{eqnarray} is discussed.
Keywords: Jacobian equations, regularity., simultaneous resolution.
Mathematics Subject Classification: 35F5.
Citation: Bernard Dacorogna, Olivier Kneuss. Multiple Jacobian equations. Communications on Pure & Applied Analysis, 2014, 13 (5) : 1779-1787. doi: 10.3934/cpaa.2014.13.1779
References:
[1]

G. Csató, B. Dacorogna and O. Kneuss, The Pullback Equation for Differential Forms, Birkhäuser/Springer, New York, 2012. doi: 10.1007/978-0-8176-8313-9.  Google Scholar

[2]

B. Dacorogna and N. Fusco, Semi-continuité des fonctionnelles avec contraintes du type $\det\nabla u>0$, Boll. Un. Mat. Ital., 4-B (1985), 179-189.  Google Scholar

[3]

B. Dacorogna and J. Moser, On a partial differential equation involving the Jacobian determinant, Ann. Inst. H. Poincaré Anal. Non Linéaire, 7 (1990), 1-26.  Google Scholar

[4]

J. Moser J, On the volume elements on a manifold, Trans. Amer. Math. Soc., 120 (1965), 286-294.  Google Scholar

show all references

References:
[1]

G. Csató, B. Dacorogna and O. Kneuss, The Pullback Equation for Differential Forms, Birkhäuser/Springer, New York, 2012. doi: 10.1007/978-0-8176-8313-9.  Google Scholar

[2]

B. Dacorogna and N. Fusco, Semi-continuité des fonctionnelles avec contraintes du type $\det\nabla u>0$, Boll. Un. Mat. Ital., 4-B (1985), 179-189.  Google Scholar

[3]

B. Dacorogna and J. Moser, On a partial differential equation involving the Jacobian determinant, Ann. Inst. H. Poincaré Anal. Non Linéaire, 7 (1990), 1-26.  Google Scholar

[4]

J. Moser J, On the volume elements on a manifold, Trans. Amer. Math. Soc., 120 (1965), 286-294.  Google Scholar

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