On a partial differential equation involving the jacobian determinant

Bernard Dacorogna; Jürgen Moser

Annales de l'I.H.P. Analyse non linéaire (1990)

  • Volume: 7, Issue: 1, page 1-26
  • ISSN: 0294-1449

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Dacorogna, Bernard, and Moser, Jürgen. "On a partial differential equation involving the jacobian determinant." Annales de l'I.H.P. Analyse non linéaire 7.1 (1990): 1-26. <http://eudml.org/doc/78211>.

@article{Dacorogna1990,
author = {Dacorogna, Bernard, Moser, Jürgen},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {volume preserving diffeomorphism; Jacobian determinant},
language = {eng},
number = {1},
pages = {1-26},
publisher = {Gauthier-Villars},
title = {On a partial differential equation involving the jacobian determinant},
url = {http://eudml.org/doc/78211},
volume = {7},
year = {1990},
}

TY - JOUR
AU - Dacorogna, Bernard
AU - Moser, Jürgen
TI - On a partial differential equation involving the jacobian determinant
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1990
PB - Gauthier-Villars
VL - 7
IS - 1
SP - 1
EP - 26
LA - eng
KW - volume preserving diffeomorphism; Jacobian determinant
UR - http://eudml.org/doc/78211
ER -

References

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  2. [A] S. Alpern, New Proofs that Weak Mixing is Generic, Inventiones Math., Vol. 32, 1976, pp. 263-279. Zbl0338.28012MR402005
  3. [AK] D.V. Anosov and A.B. Katok, New Examples in Smooth Ergodic Theory. Ergodic Diffeomorphisms, Trudy Moskov Mat. Obsc. Tom, Vol. 23, 1970, Trans. Moscow Math. Soc., Vol. 23, 1970, pp. 1-35. Zbl0255.58007MR370662
  4. [B] A. Banyaga, Formes volume sur les variétés à bord, Enseignement Math., Vol. 20, 1974, pp. 127-131. Zbl0281.58001MR358649
  5. [CL] E.A. Coddington and N. Levinson, Theory of Ordinary Differential Equations, MacGraw-Hill, New York, 1955. Zbl0064.33002MR69338
  6. [D] B. Dacorogna, A Relaxation Theorem and its Application to the Equilibrium of Gases, Arch. Ration. Mech. Anal., Vol. 77, 1981, pp. 359-385. Zbl0492.49002MR642553
  7. [GS] R.E. Greene and K. Shiohama, Diffeomorphisms and Volume Preserving Embeddings of Non Compact Manifolds, Trans. Am. Math. Soc., Vol. 255, 1979, pp. 403- 414. Zbl0418.58002MR542888
  8. [H] L. Hörmander, The Boundary Problems of Physical Geodesy, Arch. Ration. Mech. Anal., Vol. 62, 1976, pp. 1-52. Zbl0331.35020MR602181
  9. [LU] O.A. Ladyzhenskaya and N.N. Uraltseva, Linear and Quasilinear Elliptic Equations, Academic Press, New York, 1968. Zbl0164.13002MR244627
  10. [L] A.E.H. Love, Treatise on the Mathematical Theory of Elasticity, New York, 1944. Zbl0063.03651
  11. [MO] G.H. Meisters and C. Olech, Locally One to One Mappings and a Classical Theorem on Schlicht Functions, Duke Math. J., Vol. 30, 1963, pp. 63-80. Zbl0112.37702MR143921
  12. [M] J. Moser, On the Volume Elements on a Manifold, Trans. Am. Math. Soc., Vol. 120, 1965, pp. 286-294. Zbl0141.19407MR182927
  13. [T] L. Tartar, private communication, 1979. 
  14. [Z] E. Zehnder, Note on Smoothing Symplectic and Volume Preserving Diffeomorphisms, Springer, Lect. Notes Math., Vol. 597, 1976, pp. 828-855. Zbl0363.58004MR467846

Citations in EuDML Documents

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  1. Silvia Bertirotti, Roberto Van der Putten, Existence of minimizers and lower semicontinuity of integral functionals in the vectorial case
  2. Vanderlei Horita, Ali Tahzibi, Partial hyperbolicity for symplectic diffeomorphisms
  3. Dong Ye, Prescribing the jacobian determinant in Sobolev spaces
  4. Stefan Müller, On the singular support of the distributional determinant
  5. Sergio Conti, Camillo de Lellis, Remarks on the theory of elasticity
  6. P. Delanoë, Classical solvability in dimension two of the second boundary-value problem associated with the Monge-Ampère operator
  7. S. Bandyopadhyay, B. Dacorogna, On the pullback equation φ * g = f
  8. Dong Ye, Prescription de la forme volume
  9. Jeff Hogan, Chun Li, Alan McIntosh, Kewei Zhang, Global higher integrability of jacobians on bounded domains
  10. Tadeusz Iwaniec, Nonlinear analysis and quasiconformal mappings from the perspective of PDEs

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