Global higher integrability of jacobians on bounded domains

Jeff Hogan; Chun Li; Alan McIntosh; Kewei Zhang

Annales de l'I.H.P. Analyse non linéaire (2000)

  • Volume: 17, Issue: 2, page 193-217
  • ISSN: 0294-1449

How to cite

top

Hogan, Jeff, et al. "Global higher integrability of jacobians on bounded domains." Annales de l'I.H.P. Analyse non linéaire 17.2 (2000): 193-217. <http://eudml.org/doc/78491>.

@article{Hogan2000,
author = {Hogan, Jeff, Li, Chun, McIntosh, Alan, Zhang, Kewei},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Jacobians; Sobolev space; Hardy space; higher integrability; compensated compactness; differential forms},
language = {eng},
number = {2},
pages = {193-217},
publisher = {Gauthier-Villars},
title = {Global higher integrability of jacobians on bounded domains},
url = {http://eudml.org/doc/78491},
volume = {17},
year = {2000},
}

TY - JOUR
AU - Hogan, Jeff
AU - Li, Chun
AU - McIntosh, Alan
AU - Zhang, Kewei
TI - Global higher integrability of jacobians on bounded domains
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2000
PB - Gauthier-Villars
VL - 17
IS - 2
SP - 193
EP - 217
LA - eng
KW - Jacobians; Sobolev space; Hardy space; higher integrability; compensated compactness; differential forms
UR - http://eudml.org/doc/78491
ER -

References

top
  1. [1] Adams R.A., Sobolev Spaces, Academic Press, New York, 1975. Zbl0314.46030MR450957
  2. [2] Ball J.M., Murat F., W1,p-quasiconvexity and variational problems for multiple integrals, J. Funct. Anal.58 (1984) 225-253. Zbl0549.46019MR759098
  3. [3] Bennett C., Sharpley R., Interpolation of Operators, Academic Press, Boston, 1988. Zbl0647.46057MR928802
  4. [4] Brézis H., Fusco N., Sbordone C., Integrability for the Jacobian of orientation-preserving mappings, J. Funct. Anal.115 (2) (1993) 425-431. Zbl0847.26012MR1234399
  5. [5] Chang D.-C., Krantz S.G., Stein E.M., Hp Theory on a smooth domain in RN and elliptic boundary problems, J. Funct. Anal.114 (1993) 286-347. Zbl0804.35027MR1223705
  6. [6] Coifman R., Lions P.-L., Meyer Y., Semmes S., Compensated compactness and Hardy spaces, J. Math. Pures Appl.72 (1993) 247-286. Zbl0864.42009MR1225511
  7. [7] Dacorogna B., Weak continuity and weak lower semicontinuity of nonlinear functionals, in: Lect. Notes Math., Vol. 922, Springer, Berlin, 1982. Zbl0484.46041MR658130
  8. [8] Dacorogna B., Moser J., On a partial differential equation involving the Jacobian determinant, Ann. Inst. H. Poincaré Anal. Non Lineaire7 (1990) 1-26. Zbl0707.35041MR1046081
  9. [9] Ekeland I., Temam R., Convex Analysis and Variational Problems, North-Holland, Amsterdam, 1976. [10] Greco L., Iwaniec T., Moscariello G., Limits on the improved integrability of the volume forms, Indiana Univ. Math. J.44 (1995) 305-339. [11] Iwaniec T., Integrability theory of the Jacobians, Vorlesungsreihe Rheinische Friedrich-Wilhelms-UniversitätBonn36 (1995). MR463994
  10. [12] Iwaniec T., Sbordone C., On the integrability of the Jacobian under minimal hypotheses, Arch. Rational Mech. Anal.119 (1992) 129-143. Zbl0766.46016MR1176362
  11. [13] Jones P., Journé J.L., On weak convergence in H1 (Rd), Proc. Amer. Math. Soc.120 (1994) 137-138. Zbl0814.42011MR1159172
  12. [14] Lacroix M.-T., Espaces de traces ses espaces de Sobolev-Orlicz, J. de Math. Pures et Appl.53 (1974) 439-458. Zbl0275.46027MR374897
  13. [15] Montgomery-Smith S., The cotype of operators from C(K), Ph.D. Thesis, Cambridge, 1989. Zbl0701.47006
  14. [16] Montgomery-Smith S., Comparison of Orlicz-Lorentz spaces, Studia Math.103 (1993) 161-189. Zbl0814.46023MR1199324
  15. [17] Müller S., Higher integrability of determinants and weak convergence in L1, J. Reine Angew. Math.412 (1990) 20-34. Zbl0713.49004MR1078998
  16. [18] O'Neil R., Fractional integration in Orlicz spaces. I, Trans. Amer. Math. Soc.115 (1965) 300-328. Zbl0132.09201MR194881
  17. [19] Robbin J.W., Rogers R.C., Temple B., On weak continuity and the Hodge decomposition, Trans. Amer. Math. Soc.303 (1987) 609-618. Zbl0634.35005MR902788
  18. [20] Rogers R.C., Temple B., A characterization of the weakly continuous polynomials in the method of compensated compactness, Trans. Amer. Math. Soc.310 (1988) 405-417. Zbl0706.46009MR965761
  19. [21] Semmes S., A primer on Hardy spaces, and some remarks on a theorem of Evans and Müller, Comm. Partial Differential Equations19 (1994) 277-319. Zbl0836.35030MR1257006
  20. [22] Stein E.M., Note on the class L log L, Studia Math.32 (1969) 305-310. Zbl0182.47803MR247534
  21. [23] Stein E.M., Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton, 1970. Zbl0207.13501MR290095
  22. [24] Ye D., Prescribingthe Jacobian determinant in Sobolev spaces, Ann. Inst. Henri Poincare (Analyse non lineaire)11 (3) (1994) 275-296. Zbl0834.35047MR1277896

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.