On the Pullback Equation φ * g=f
Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 5, pp. 1717-1741.
@article{AIHPC_2009__26_5_1717_0,
     author = {Bandyopadhyay, S. and Dacorogna, B.},
     title = {On the {Pullback} {Equation} ${\phi }^{*}\left(g\right)=f$},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1717--1741},
     publisher = {Elsevier},
     volume = {26},
     number = {5},
     year = {2009},
     doi = {10.1016/j.anihpc.2008.10.006},
     mrnumber = {2566707},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2008.10.006/}
}
TY  - JOUR
AU  - Bandyopadhyay, S.
AU  - Dacorogna, B.
TI  - On the Pullback Equation ${\phi }^{*}\left(g\right)=f$
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2009
SP  - 1717
EP  - 1741
VL  - 26
IS  - 5
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.anihpc.2008.10.006/
DO  - 10.1016/j.anihpc.2008.10.006
LA  - en
ID  - AIHPC_2009__26_5_1717_0
ER  - 
%0 Journal Article
%A Bandyopadhyay, S.
%A Dacorogna, B.
%T On the Pullback Equation ${\phi }^{*}\left(g\right)=f$
%J Annales de l'I.H.P. Analyse non linéaire
%D 2009
%P 1717-1741
%V 26
%N 5
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.anihpc.2008.10.006/
%R 10.1016/j.anihpc.2008.10.006
%G en
%F AIHPC_2009__26_5_1717_0
Bandyopadhyay, S.; Dacorogna, B. On the Pullback Equation ${\phi }^{*}\left(g\right)=f$. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 5, pp. 1717-1741. doi : 10.1016/j.anihpc.2008.10.006. http://www.numdam.org/articles/10.1016/j.anihpc.2008.10.006/

[1] Abraham R., Marsden J. E., Ratiu T., Manifolds, Tensor Analysis, and Applications, second ed., Springer-Verlag, New York, 1988. | MR | Zbl

[2] Banyaga A., Formes-Volume Sur Les Variétés À Bord, Enseignement Math. 20 (1974) 127-131. | MR | Zbl

[3] Burago D., Kleiner B., Separated Nets in Euclidean Space and Jacobian of BiLipschitz Maps, Geom. Funct. Anal. 8 (1998) 273-282. | MR | Zbl

[4] Dacorogna B., A Relaxation Theorem and Its Applications to the Equilibrium of Gases, Arch. Ration. Mech. Anal. 77 (1981) 359-386. | MR | Zbl

[5] Dacorogna B., Existence and Regularity of Solutions of dω=f With Dirichlet Boundary Conditions, in: Nonlinear Problems in Mathematical Physics and Related Topics, I, Int. Math. Ser. (N.Y.), vol. 1, Kluwer/Plenum, New York, 2002, pp. 67-82. | MR | Zbl

[6] Dacorogna B., Direct Methods in the Calculus of Variations, second ed., Springer-Verlag, New York, 2007. | MR | Zbl

[7] Dacorogna B., Moser J., On a Partial Differential Equation Involving the Jacobian Determinant, Ann. Inst. H. Poincaré Anal. Non Linéaire 7 (1990) 1-26. | Numdam | MR | Zbl

[8] Duff G. F., Spencer D. C., Harmonic Tensors on Riemannian Manifolds With Boundary, Ann. of Math. 56 (1952) 128-156. | MR | Zbl

[9] Hörmander L., The Boundary Problems of Physical Geodesy, Arch. Ration. Mech. Anal. 62 (1976) 1-52. | MR | Zbl

[10] Kress R., Potentialtheoretische Randwertprobleme Bei Tensorfeldern Beliebiger Dimension Und Beliebigen Ranges, Arch. Ration. Mech. Anal. 47 (1972) 59-80. | MR | Zbl

[11] Mcduff D., Salamon D., Introduction to Symplectic Topology, second ed., Oxford Science Publications, Oxford, 1998. | MR | Zbl

[12] Mcmullen C. T., Lipschitz Maps and Nets in Euclidean Space, Geom. Funct. Anal. 8 (1998) 304-314. | MR | Zbl

[13] Moser J., On the Volume Elements on a Manifold, Trans. Amer. Math. Soc. 120 (1965) 286-294. | MR | Zbl

[14] Reimann H. M., Harmonische Funktionen Und Jacobi-Determinanten Von Diffeomorphismen, Comment. Math. Helv. 47 (1972) 397-408. | MR | Zbl

[15] Rivière T., Ye D., Resolutions of the Prescribed Volume Form Equation, NoDEA Nonlinear Differential Equations Appl. 3 (1996) 323-369. | MR | Zbl

[16] L. Tartar, unpublished, 1978.

[17] Taylor M. E., Partial Differential Equations, Vol. 1, Springer-Verlag, New York, 1996. | Zbl

[18] Ye D., Prescribing the Jacobian Determinant in Sobolev Spaces, Ann. Inst. H. Poincaré Anal. Non Linéaire 11 (1994) 275-296. | Numdam | MR | Zbl

[19] Zehnder E., Note on Smoothing Symplectic and Volume Preserving Diffeomorphisms, in: Lecture Notes in Mathematics, vol. 597, Springer-Verlag, Berlin, 1976, pp. 828-855. | MR | Zbl

Cité par Sources :