On the pullback equation φ * g = f

S. Bandyopadhyay; B. Dacorogna

Annales de l'I.H.P. Analyse non linéaire (2009)

  • Volume: 26, Issue: 5, page 1717-1741
  • ISSN: 0294-1449

How to cite

top

Bandyopadhyay, S., and Dacorogna, B.. "On the pullback equation ${\phi }^{*}\left(g\right)=f$." Annales de l'I.H.P. Analyse non linéaire 26.5 (2009): 1717-1741. <http://eudml.org/doc/78910>.

@article{Bandyopadhyay2009,
author = {Bandyopadhyay, S., Dacorogna, B.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Darboux theorem; symplectic forms; Hölder regularity},
language = {eng},
number = {5},
pages = {1717-1741},
publisher = {Elsevier},
title = {On the pullback equation $\{\phi \}^\{*\}\left(g\right)=f$},
url = {http://eudml.org/doc/78910},
volume = {26},
year = {2009},
}

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
PB - Elsevier
VL - 26
IS - 5
SP - 1717
EP - 1741
LA - eng
KW - Darboux theorem; symplectic forms; Hölder regularity
UR - http://eudml.org/doc/78910
ER -

References

top
  1. [1] Abraham R., Marsden J.E., Ratiu T., Manifolds, Tensor Analysis, and Applications, second ed., Springer-Verlag, New York, 1988. Zbl0875.58002MR960687
  2. [2] Banyaga A., Formes-volume sur les variétés à bord, Enseignement Math.20 (1974) 127-131. Zbl0281.58001MR358649
  3. [3] Burago D., Kleiner B., Separated nets in Euclidean space and Jacobian of biLipschitz maps, Geom. Funct. Anal.8 (1998) 273-282. Zbl0902.26004MR1616135
  4. [4] Dacorogna B., A relaxation theorem and its applications to the equilibrium of gases, Arch. Ration. Mech. Anal.77 (1981) 359-386. Zbl0492.49002MR642553
  5. [5] Dacorogna B., Existence and regularity of solutions of d ω = 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. Zbl1148.35306MR1970605
  6. [6] Dacorogna B., Direct Methods in the Calculus of Variations, second ed., Springer-Verlag, New York, 2007. Zbl1140.49001MR990890
  7. [7] Dacorogna B., Moser J., On a partial differential equation involving the Jacobian determinant, Ann. Inst. H. Poincaré Anal. Non Linéaire7 (1990) 1-26. Zbl0707.35041MR1046081
  8. [8] Duff G.F., Spencer D.C., Harmonic tensors on Riemannian manifolds with boundary, Ann. of Math.56 (1952) 128-156. Zbl0049.18901MR48137
  9. [9] Hörmander L., The boundary problems of physical geodesy, Arch. Ration. Mech. Anal.62 (1976) 1-52. Zbl0331.35020MR602181
  10. [10] Kress R., Potentialtheoretische Randwertprobleme bei Tensorfeldern beliebiger Dimension und beliebigen Ranges, Arch. Ration. Mech. Anal.47 (1972) 59-80. Zbl0238.31010MR361131
  11. [11] McDuff D., Salamon D., Introduction to Symplectic Topology, second ed., Oxford Science Publications, Oxford, 1998. Zbl0844.58029MR1702941
  12. [12] McMullen C.T., Lipschitz maps and nets in Euclidean space, Geom. Funct. Anal.8 (1998) 304-314. Zbl0941.37030MR1616159
  13. [13] Moser J., On the volume elements on a manifold, Trans. Amer. Math. Soc.120 (1965) 286-294. Zbl0141.19407MR182927
  14. [14] Reimann H.M., Harmonische Funktionen und Jacobi-Determinanten von Diffeomorphismen, Comment. Math. Helv.47 (1972) 397-408. Zbl0249.57016MR315064
  15. [15] Rivière T., Ye D., Resolutions of the prescribed volume form equation, NoDEA Nonlinear Differential Equations Appl.3 (1996) 323-369. Zbl0857.35025MR1404587
  16. [16] L. Tartar, unpublished, 1978. 
  17. [17] Taylor M.E., Partial Differential Equations, vol. 1, Springer-Verlag, New York, 1996. Zbl0869.35003
  18. [18] Ye D., Prescribing the Jacobian determinant in Sobolev spaces, Ann. Inst. H. Poincaré Anal. Non Linéaire11 (1994) 275-296. Zbl0834.35047MR1277896
  19. [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. Zbl0363.58004MR467846

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.