Global higher integrability of jacobians on bounded domains
Hogan, Jeff ; Li, Chun ; McIntosh, Alan ; Zhang, Kewei
Annales de l'I.H.P. Analyse non linéaire, Tome 17 (2000), p. 193-217 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 2000-01-01
@article{AIHPC_2000__17_2_193_0,
     author = {Hogan, Jeff and Li, Chun and McIntosh, Alan and Zhang, Kewei},
     title = {Global higher integrability of jacobians on bounded domains},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {17},
     year = {2000},
     pages = {193-217},
     mrnumber = {1753093},
     zbl = {1008.42014},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2000__17_2_193_0}
}

Hogan, Jeff; Li, Chun; McIntosh, Alan; Zhang, Kewei. Global higher integrability of jacobians on bounded domains. Annales de l'I.H.P. Analyse non linéaire, Tome 17 (2000) pp. 193-217. http://gdmltest.u-ga.fr/item/AIHPC_2000__17_2_193_0/

[1] Adams R.A., Sobolev Spaces, Academic Press, New York, 1975. | MR 450957 | Zbl 0314.46030

[2] Ball J.M., Murat F., W1,p-quasiconvexity and variational problems for multiple integrals, J. Funct. Anal. 58 (1984) 225-253. | MR 759098 | Zbl 0549.46019

[3] Bennett C., Sharpley R., Interpolation of Operators, Academic Press, Boston, 1988. | MR 928802 | Zbl 0647.46057

[4] Brézis H., Fusco N., Sbordone C., Integrability for the Jacobian of orientation-preserving mappings, J. Funct. Anal. 115 (2) (1993) 425-431. | MR 1234399 | Zbl 0847.26012

[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. | MR 1223705 | Zbl 0804.35027

[6] Coifman R., Lions P.-L., Meyer Y., Semmes S., Compensated compactness and Hardy spaces, J. Math. Pures Appl. 72 (1993) 247-286. | MR 1225511 | Zbl 0864.42009

[7] Dacorogna B., Weak continuity and weak lower semicontinuity of nonlinear functionals, in: Lect. Notes Math., Vol. 922, Springer, Berlin, 1982. | MR 658130 | Zbl 0484.46041

[8] Dacorogna B., Moser J., On a partial differential equation involving the Jacobian determinant, Ann. Inst. H. Poincaré Anal. Non Lineaire 7 (1990) 1-26. | Numdam | MR 1046081 | Zbl 0707.35041

[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-Universität Bonn 36 (1995). | MR 463994

[12] Iwaniec T., Sbordone C., On the integrability of the Jacobian under minimal hypotheses, Arch. Rational Mech. Anal. 119 (1992) 129-143. | MR 1176362 | Zbl 0766.46016

[13] Jones P., Journé J.L., On weak convergence in H1 (Rd), Proc. Amer. Math. Soc. 120 (1994) 137-138. | MR 1159172 | Zbl 0814.42011

[14] Lacroix M.-T., Espaces de traces ses espaces de Sobolev-Orlicz, J. de Math. Pures et Appl.53 (1974) 439-458. | MR 374897 | Zbl 0275.46027

[15] Montgomery-Smith S., The cotype of operators from C(K), Ph.D. Thesis, Cambridge, 1989.

[16] Montgomery-Smith S., Comparison of Orlicz-Lorentz spaces, Studia Math. 103 (1993) 161-189. | MR 1199324 | Zbl 0814.46023

[17] Müller S., Higher integrability of determinants and weak convergence in L1, J. Reine Angew. Math. 412 (1990) 20-34. | MR 1078998 | Zbl 0713.49004

[18] O'Neil R., Fractional integration in Orlicz spaces. I, Trans. Amer. Math. Soc. 115 (1965) 300-328. | MR 194881 | Zbl 0132.09201

[19] Robbin J.W., Rogers R.C., Temple B., On weak continuity and the Hodge decomposition, Trans. Amer. Math. Soc. 303 (1987) 609-618. | MR 902788 | Zbl 0634.35005

[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. | MR 965761 | Zbl 0706.46009

[21] Semmes S., A primer on Hardy spaces, and some remarks on a theorem of Evans and Müller, Comm. Partial Differential Equations 19 (1994) 277-319. | MR 1257006 | Zbl 0836.35030

[22] Stein E.M., Note on the class L log L, Studia Math. 32 (1969) 305-310. | MR 247534 | Zbl 0182.47803

[23] Stein E.M., Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton, 1970. | MR 290095 | Zbl 0207.13501

[24] Ye D., Prescribing the Jacobian determinant in Sobolev spaces, Ann. Inst. Henri Poincare (Analyse non lineaire) 11 (3) (1994) 275-296. | Numdam | MR 1277896 | Zbl 0834.35047