Viene messo in evidenza il ruolo essenziale degli spazi di Sobolev generalizzati nello studio della proprietà (N) di Lusin per omeomorfismi tra aperti di .
@article{BUMI_2012_9_5_3_727_0,
author = {L. D'Onofrio and C. Sbordone and R. Schiattarella},
title = {Propriet\`a di misurabilit\`a di un omeomorfismo in ipotesi minimali di integrabilit\`a per il gradiente},
journal = {Bollettino dell'Unione Matematica Italiana},
volume = {5},
year = {2012},
pages = {727-730},
zbl = {1280.30010},
mrnumber = {3051742},
language = {it},
url = {http://dml.mathdoc.fr/item/BUMI_2012_9_5_3_727_0}
}
D’Onofrio, L.; Sbordone, C.; Schiattarella, R. Proprietà di misurabilità di un omeomorfismo in ipotesi minimali di integrabilità per il gradiente. Bollettino dell'Unione Matematica Italiana, Tome 5 (2012) pp. 727-730. http://gdmltest.u-ga.fr/item/BUMI_2012_9_5_3_727_0/
[1] , Generalized N-property and Sard Theorem for Sobolev maps, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 23 (2012), no. 4, in corso di stampa. | MR 2999558 | Zbl 1258.35056
[2] - e , Regularity of optimal transport maps and partial differential inclusions, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 22 (2011), no. 3, 311-336. | MR 2847475 | Zbl 1241.35033
[3] , Homeomorphism with zero Jacobian: sharp integrability of the derivative, J. Math. Anal. Appl.373 (2011), no. 1, 161-174. | MR 2684467 | Zbl 1214.26008
[4] e , Orlicz-Sobolev regularity of mappings with subexponentially integrable distortion, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 20 (2009), no. 4, 301-326. | MR 2550847 | Zbl 1178.30026
[5] , e , The Grand Sobolev homeomorphisms and their measurability properties, Adv. Nonlinear Stud., in corso di stampa. | MR 3012861
[6] e , Approximation of Grand Sobolev homeomorphisms and their properties, in preparazione.
[7] , e , The limit of homeomorphism with finite distortion, Calc. Var. Partial Differential Equations 33 (2008), no. 3, 377-390. | MR 2429536 | Zbl 1157.30016
[8] , A remark on the equality , Differential Integral Equations6 (1993), 1089-1100. | MR 1230483 | Zbl 0784.49013
[9] e , A version of Gehring lemma in Orlicz spaces, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei Mat. Appl. 23, (2012), 29-50. | MR 2924890 | Zbl 1239.26015
[10] , e , Composition of bi-Sobolev homeomorphism, Proc. of the Royal Society of Edinburgh Sec. A, Mathematics, Vol. 142, (2012) 61-80. | MR 2887643 | Zbl 1272.30038
[11] , Sobolev homeomorphism with zero Jacobian almost everywhere, J. Math. Pures Appl. (9) 95 (2011), no. 4, 444-458. | MR 2776377 | Zbl 1222.26018
[12] , , e , Bisobolev mappings and elliptic equation in the plane, J. Math. Anal. Appl. 355 (2009), 22-32. | MR 2514448 | Zbl 1169.30007
[13] e , On the integrability of the Jacobian under minimal hypotheses, Arch. Mech. Anal. 119, n.2, 1992, 129-143. | MR 1176362 | Zbl 0766.46016
[14] , e , Mappings of finite distortion: condition N Michigan Math. J. Volume 49, Issue 1 (2001), 169-181. | MR 1827080 | Zbl 0997.30018
[15] , e , Luzin's Condition (N) and Sobolev mappings, to appear on Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 23 (2012) no. 4, in corso di stampa. | MR 2999556
[16] e , The regularity of the inverses of Sobolev homeomorphisms with finite distortion, J. Geom. Anal., in corso di stampa. | MR 3145933 | Zbl 1300.26009
[17] , e , Planar ACL-home- omorphisms: critical points of their components, Commun. Pure Appl. Anal. 9 (2010), no. 5, 1391-1397. | MR 2646004 | Zbl 1203.49051