Quasiharmonic fields

Iwaniec, Tadeusz ; Sbordone, Carlo

Annales de l'I.H.P. Analyse non linéaire, Tome 18 (2001), p. 519-572 / Harvested from Numdam

Détail

Publié le : 2001-01-01

MR 1849688 | Zbl 1068.30011 | 3 citations dans Numdam

Bibliographie

[1] Astala K, Area distortion of quasiconformal mappings, Acta Math. 173 (1994) 37-60. | MR 1294669 | Zbl 0815.30015

[2] Astala K, Analytic aspects of quasiconformality, in: Proc. ICM, 2, 1998, pp. 617-626. | MR 1648110 | Zbl 0906.30019

[3] Astala K., Iwaniec T., Koskela P., Martin G., Mappings of BMO-bounded distortion, Mathematische Annalen, to appear. | MR 1777116 | Zbl 0954.30009

[4] Astala K, Iwaniec T, Saksman E, The Beltrami operator, Duke Math. J. (1998).

[5] Baernstein A., Montgomery-Smith S.J., Some conjectures about integral means of ∂f and $\overline{\partial}$f, Proc. Mattsfest., to appear. | Zbl 0966.30001

[6] Bañuelos R, Lindeman A, A martingale study of the Beurling-Ahlfors transform in Rn, J. Funct. Anal. 145 (1997) 224-265. | Zbl 0876.60026

[7] Bers L, Nirenberg L, On linear and nonlinear elliptic boundary value problems in the plane, in: Cremonese (Ed.), Conv. Int.le “Eq. Lineari a Derivate Parziali” (Trieste 1954), Roma, 1955, pp. 141-167. | Zbl 0067.32504

[8] Boccardo L, Gallouet T, Nonlinear elliptic and parabolic equations involving measure data, J. Funct. Anal. 87 (1989) 149-169. | MR 1025884 | Zbl 0707.35060

[9] Bojarski B, Generalized solution of a system of first order differential equations of elliptic type with discontinuous coefficients, Math. Sb. 43 (1957) 451-503. | MR 106324

[10] Brakalova M.A, Jenkins J.A, On solutions of the Beltrami equations, J. d'Analyse Math. 76 (1998) 67-92. | MR 1676936 | Zbl 0921.30015

[11] Burkholder D, Sharp inequalities for martingales and stochastic integrals, Asterisque 157/158 (1988) 75-94. | MR 976214 | Zbl 0656.60055

[12] Caccioppoli R, Fondamenti per una teoria generale delle funzioni pseudoanalitiche di una variabile complessa, Rend, Acc. Naz. Lincei 13 (1952) 197-204. | MR 56718 | Zbl 0048.06001

[13] Carozza M, Moscariello G, Passarelli A, Linear elliptic equations with BMO coefficients, Rend. Acc. Naz. Lincei, Ser. IX X (1999) 17-23. | MR 1768517 | Zbl 1042.35009

[14] Carozza M., Moscariello G., Passarelli A., Nonlinear equations with growth coefficients in BMO, Rend. Houston J. of Math., to appear. | MR 1953694 | Zbl 1021.35001

[15] Chanillo S, Wheeden R.L, Harnack's inequality and mean value inequalities for solutions of degenerate elliptic equations, Comm. PDE 11 (10) (1986) 1111-1134. | MR 847996 | Zbl 0634.35035

[16] Chiarenza F, Frasca M, Longo P, W2,p-solvability of the Dirichlet problem for nondivergence elliptic equations with VMO-coefficients, Trans. Amer. Math. Soc. 336 (1993) 841-853. | MR 1088476 | Zbl 0818.35023

[17] 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

[18] Coifman R, Rochberg R, Another characterization of BMO, Proc. AMS 79 (2) (1980) 249-254. | MR 565349 | Zbl 0432.42016

[19] Coifman R, Rochberg R, Weiss G, Factorization theorems for Hardy spaces in several variables, Ann. Math. 103 (1976) 569-645. | MR 412721 | Zbl 0326.32011

[20] Dacorogna B, Direct Methods in the Calculus of Variations, Springer, 1989. | MR 990890 | Zbl 0703.49001

[21] David G, Solutions de l'equation de Beltrami avec ‖μ‖∞=1, Ann. Acad. Sci. Fenn. Ser. A1 Math. 13 (1988) 25-70.

[22] Del Vecchio T, Nonlinear elliptic equations with measure data, Potential Analysis 4 (2) (1995) 185-203. | MR 1323826 | Zbl 0815.35023

[23] Di Fazio G, Lp-estimates for divergence form elliptic equations with discontinuous coefficients, Boll. Un. Mat. It. 7 (1996) 409-420. | MR 1405255 | Zbl 0865.35048

[24] De Giorgi E, Unpublished manuscript, 1996.

[25] Dolzmann G, Hungerbuehler N, Müller S, Uniqueness and maximal regularity for nonlinear elliptic systems of n-Laplace type with measure valued right hand side, Preprint, 1998.

[26] Donaldson S.K, Sullivan D.P, Quasiconformal 4-manifolds, Acta Math. 163 (1989) 181-252. | MR 1032074 | Zbl 0704.57008

[27] Ekeland I, Temam R, Convex Analysis and Variational Problems, North-Holland, 1976. | MR 463994 | Zbl 0322.90046

[28] Eremenko A, Hamilton D, On the area distortion by quasiconformal mappings, Proc. Amer. Math. Soc. 123 (1995) 2793-2797. | MR 1283548 | Zbl 0841.30013

[29] Fabes E.B, Kenig C.E, Serapioni R, The local regularity of solutions of degenerate elliptic equations, Comm. Partial Diff. Equations 7 (1982) 77-116. | MR 643158 | Zbl 0498.35042

[30] Finn R, Serrin J, On the Hölder continuity of quasiconformal and elliptic mappings, Trans. Amer. Math. Soc. 89 (1958) 1-15. | MR 97626 | Zbl 0082.29401

[31] Fiorenza A, Sbordone C, Existence and uniqueness results for solutions of nonlinear equations with right hand side in L1, Studia Math. 127 (3) (1998) 223-231. | MR 1489454 | Zbl 0891.35039

[32] Franchi B, Serapioni R, Serra Cassano F, Irregular solutions of linear degenerate elliptic equations, Potential Analysis 9 (1998) 201-216. | MR 1666899 | Zbl 0919.35050

[33] Giannetti F, Verde A, Variational integrals for elliptic complexes, Studia Math. 140 (1) (2000) 79-98. | MR 1763883 | Zbl 0968.58019

[34] Greco L, Iwaniec T, Moscariello G, Limits of the improved integrability of the volume forms, Indiana Univ. Math. J. 44 (2) (1995) 305-339. | MR 1355401 | Zbl 0855.42009

[35] Greco L, Iwaniec T, Sbordone C, Inverting the p-harmonic operator, Manuscripta Math. 92 (1997) 249-258. | MR 1428651 | Zbl 0869.35037

[36] Gustavsson J, Peetre J, Interpolation of Orlicz spaces, Studia Math. LX (1977) 33-59. | MR 438102 | Zbl 0353.46019

[37] Heinonen J, Koskela P, Sobolev mappings with integrable dilatation, Arch. Rat. Mech. Anal. 125 (1993) 81-97. | MR 1241287 | Zbl 0792.30016

[38] Iwaniec T., Nonlinear Cauchy-Riemann operators in Rn, Trans. AMS, to appear. | Zbl 01721137

[39] Iwaniec T, Koskela P, Martin G, Mappings of BMO-bounded distorsion and Beltrami type operators, Preprint Univ. of Jyväskyla, 1998.

[40] Iwaniec T, Lutoborski A, Integral estimates for null Lagrangians, Arch. Rat. Mech. Anal. 125 (1993) 25-79. | MR 1241286 | Zbl 0793.58002

[41] Iwaniec T, Martin G, Quasiregular mappings in even dimension, Acta Math. 170 (1993) 29-81. | MR 1208562 | Zbl 0785.30008

[42] Iwaniec T, Martin G, Riesz Transforms and related singular integrals, J. Reine Angew. Math. 473 (1996) 25-57. | MR 1390681 | Zbl 0847.42015

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

[44] Iwaniec T, Sbordone C, Riesz transforms and elliptic pde's with VMO coefficients, J. d'Analyse Math. 74 (1998) 183-212. | MR 1631658 | Zbl 0909.35039

[45] Iwaniec T, Sbordone C, Div-curl fields of finite distorsion, C.R. Acad. Sci. Paris, Serie I 327 (1998) 729-734. | MR 1660033 | Zbl 0916.30015

[46] Iwaniec T, Scott C, Stroffolini B, Nonlinear Hodge theory on manifolds with boundary, Annali di Matematica pura ed applicata (IV) CLXXV (1999) 37-115. | MR 1747627 | Zbl 0963.58003

[47] Iwaniec T, Šverák V, On mappings with integrable dilatation, Proc. Amer. Math. Soc. 118 (1993) 181-188. | MR 1160301 | Zbl 0784.30015

[48] Iwaniec T, Verde A, A study of Jacobians in Hardy-Orlicz spaces, Proc. Roy. Soc. Edinburgh 29A (1999) 539-570. | Zbl 0954.46018

[49] John O, Malý J, Stará J, Nowhere continuous solutions to elliptic systems, Comm. Math. Univ. Carolinae 30 (1) (1989) 33-43. | MR 995699 | Zbl 0691.35024

[50] Kilpeläinen T, Malý J, Degenerate elliptic equations with measure data and nonlinear potentials, Ann. Scuola Norm. Sup. Pisa, Ser. IV 19 (1992) 591-613. | Numdam | MR 1205885 | Zbl 0797.35052

[51] Koskela P, Manfredi J, Villamore E, Regularity theory and traces of A̧-harmonic functions, Trans. Amer. Math. Soc. 348 (2) (1996) 755-766. | Zbl 0849.31015

[52] Krasnosel'Skii M.A, Rutickii Yu.B, Convex Functions and Orlicz spaces, P. Noordhoff Ltd, Groningen, 1961, translation. | MR 126722 | Zbl 0095.09103

[53] Leonetti F, Nesi V, Quasiconformal solutions to certain first order systems and the proof of a conjecture of G.W. Milton, J. Math. Pures Appl. 76 (1997) 1-16. | MR 1432370 | Zbl 0869.35019

[54] Manfredi J, Villamor E, Mappings with integrable dilatation in higher dimensions, Bull. Amer. Math. Soc. 32 (1995) 235-240. | MR 1313107 | Zbl 0857.30020

[55] Meyers N, An Lp-estimate for the gradient of solutions of second order elliptic divergence equations, Ann. Sc. Norm. Sup. Pisa 17 (1963) 189-206. | Numdam | MR 159110 | Zbl 0127.31904

[56] Migliaccio L., Moscariello G., Higher integrability of Div-Curl Products (1997), Ricerche di Matematica, to appear. | MR 1795037

[57] Iwaniec T., Migliaccio L., Moscariello G., Passarelli di Napoli A., Integrability Theory of Nonlinear Elliptic Complexes, to appear.

[58] Modica G, Quasiminimi di alcuni funzionali degeneri, Annali di Matematica (1984) 121-143. | Zbl 0596.49008

[59] Moscariello G, On the integrability of the Jacobian in Orlicz spaces, Math. Japonica 40 (2) (1994) 323-329. | MR 1297249 | Zbl 0805.46026

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

[61] Murat F, Equations non linéaires avec second membre L1 on mésure, Preprint, 1994.

[62] Palagachev D.K, Quasilinear elliptic equations with VMO coefficients, Trans. Amer. Math. Soc. 347 (1995) 2481-2493. | MR 1308019 | Zbl 0833.35048

[63] Rao M.M, Ren Z.D, Theory of Orlicz Spaces, Marcel Dekker, New York, 1991. | MR 1113700 | Zbl 0724.46032

[64] Ryazanov V, Srebro U, Yakubov E, BMO-quasiconformal mappings, Preprint 155, University of Helsinki, August 1997. | MR 1828484

[65] Sbordone C, New estimates for div-curl products and very weak solutions of pde's, Ann. Scuola Norm. Sup. Pisa IV XXV (4) (1997) 739-756. | Numdam | MR 1655540 | Zbl 1073.35515

[66] Serrin J, Pathological solutions of elliptic differential equations, Ann. Sc. Norm. Sup. Pisa 18 (1964) 385-387. | Numdam | MR 170094 | Zbl 0142.37601

[67] Souček J, Singular solutions to linear elliptic systems, Comm. Math. Univ. Carolinae 25 (1984) 273-281. | MR 768815 | Zbl 0564.35008

[68] Stampacchia G, Le probléme de Dirichlet pour les equations elliptiques du second ordre a coefficients discontinus, Ann. Inst. Fourier, Grenoble 15 (1965) 189-258. | Numdam | MR 192177 | Zbl 0151.15401

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

[70] Stein E, Harmonic Analysis, Princeton University Press, 1993. | MR 1232192 | Zbl 0821.42001

[71] Šverák V, Rank-one convexity does not imply quasiconvexity, Proc. Royal Soc. Edinburgh 120A (1992) 185-189. | MR 1149994 | Zbl 0777.49015

[72] Trudinger N, On the regularity of generalized solutions of linear nonuniformly elliptic equations, Arch. Rat. Mech. Anal. 42 (1971) 51-62. | MR 344656 | Zbl 0218.35035

[73] Tukia P, Compactness properties of μ-homeomorphisms, Ann. Acad. Sci., Ser. A1 Math. 16 (1991) 47-69. | Zbl 0692.30017

[74] Vekua I.N., Generalized Analytic Functions, Pure and Applied Mathematics, Vol. 25, Pergamon Press, Oxford. | MR 108572 | Zbl 0100.07603