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Multiple Jacobian equations

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  • 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.
    Mathematics Subject Classification: 35F50.


    \begin{equation} \\ \end{equation}
  • [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.


    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.


    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.


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

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