Quasiharmonic fields

Tadeusz Iwaniec; Carlo Sbordone

Annales de l'I.H.P. Analyse non linéaire (2001)

  • Volume: 18, Issue: 5, page 519-572
  • ISSN: 0294-1449

How to cite

top

Iwaniec, Tadeusz, and Sbordone, Carlo. "Quasiharmonic fields." Annales de l'I.H.P. Analyse non linéaire 18.5 (2001): 519-572. <http://eudml.org/doc/78530>.

@article{Iwaniec2001,
author = {Iwaniec, Tadeusz, Sbordone, Carlo},
journal = {Annales de l'I.H.P. Analyse non linéaire},
language = {eng},
number = {5},
pages = {519-572},
publisher = {Elsevier},
title = {Quasiharmonic fields},
url = {http://eudml.org/doc/78530},
volume = {18},
year = {2001},
}

TY - JOUR
AU - Iwaniec, Tadeusz
AU - Sbordone, Carlo
TI - Quasiharmonic fields
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2001
PB - Elsevier
VL - 18
IS - 5
SP - 519
EP - 572
LA - eng
UR - http://eudml.org/doc/78530
ER -

References

top
  1. [1] Astala K, Area distortion of quasiconformal mappings, Acta Math.173 (1994) 37-60. Zbl0815.30015MR1294669
  2. [2] Astala K, Analytic aspects of quasiconformality, in: Proc. ICM, 2, 1998, pp. 617-626. Zbl0906.30019MR1648110
  3. [3] Astala K., Iwaniec T., Koskela P., Martin G., Mappings of BMO-bounded distortion, Mathematische Annalen, to appear. Zbl0954.30009MR1777116
  4. [4] Astala K, Iwaniec T, Saksman E, The Beltrami operator, Duke Math. J. (1998). 
  5. [5] Baernstein A., Montgomery-Smith S.J., Some conjectures about integral means of ∂fand ¯ f, Proc. Mattsfest., to appear. Zbl0966.30001
  6. [6] Bañuelos R, Lindeman A, A martingale study of the Beurling–Ahlfors transform in Rn, J. Funct. Anal.145 (1997) 224-265. Zbl0876.60026
  7. [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. Zbl0067.32504
  8. [8] Boccardo L, Gallouet T, Nonlinear elliptic and parabolic equations involving measure data, J. Funct. Anal.87 (1989) 149-169. Zbl0707.35060MR1025884
  9. [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. MR106324
  10. [10] Brakalova M.A, Jenkins J.A, On solutions of the Beltrami equations, J. d'Analyse Math.76 (1998) 67-92. Zbl0921.30015MR1676936
  11. [11] Burkholder D, Sharp inequalities for martingales and stochastic integrals, Asterisque157/158 (1988) 75-94. Zbl0656.60055MR976214
  12. [12] Caccioppoli R, Fondamenti per una teoria generale delle funzioni pseudoanalitiche di una variabile complessa, Rend, Acc. Naz. Lincei13 (1952) 197-204. Zbl0048.06001MR56718
  13. [13] Carozza M, Moscariello G, Passarelli A, Linear elliptic equations with BMO coefficients, Rend. Acc. Naz. Lincei, Ser. IXX (1999) 17-23. Zbl1042.35009MR1768517
  14. [14] Carozza M., Moscariello G., Passarelli A., Nonlinear equations with growth coefficients in BMO, Rend. Houston J. of Math., to appear. Zbl1021.35001MR1953694
  15. [15] Chanillo S, Wheeden R.L, Harnack's inequality and mean value inequalities for solutions of degenerate elliptic equations, Comm. PDE11 (10) (1986) 1111-1134. Zbl0634.35035MR847996
  16. [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. Zbl0818.35023MR1088476
  17. [17] Coifman R, Lions P.L, Meyer Y, Semmes S, Compensated compactness and Hardy spaces, J. Math. Pures Appl.72 (1993) 247-286. Zbl0864.42009MR1225511
  18. [18] Coifman R, Rochberg R, Another characterization of BMO, Proc. AMS79 (2) (1980) 249-254. Zbl0432.42016MR565349
  19. [19] Coifman R, Rochberg R, Weiss G, Factorization theorems for Hardy spaces in several variables, Ann. Math.103 (1976) 569-645. Zbl0326.32011MR412721
  20. [20] Dacorogna B, Direct Methods in the Calculus of Variations, Springer, 1989. Zbl0703.49001MR990890
  21. [21] David G, Solutions de l'equation de Beltrami avec ‖μ‖∞=1, Ann. Acad. Sci. Fenn. Ser. A1 Math.13 (1988) 25-70. 
  22. [22] Del Vecchio T, Nonlinear elliptic equations with measure data, Potential Analysis4 (2) (1995) 185-203. Zbl0815.35023MR1323826
  23. [23] Di Fazio G, Lp-estimates for divergence form elliptic equations with discontinuous coefficients, Boll. Un. Mat. It.7 (1996) 409-420. Zbl0865.35048MR1405255
  24. [24] De Giorgi E, Unpublished manuscript, 1996. 
  25. [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. [26] Donaldson S.K, Sullivan D.P, Quasiconformal 4-manifolds, Acta Math.163 (1989) 181-252. Zbl0704.57008MR1032074
  27. [27] Ekeland I, Temam R, Convex Analysis and Variational Problems, North-Holland, 1976. Zbl0322.90046MR463994
  28. [28] Eremenko A, Hamilton D, On the area distortion by quasiconformal mappings, Proc. Amer. Math. Soc.123 (1995) 2793-2797. Zbl0841.30013MR1283548
  29. [29] Fabes E.B, Kenig C.E, Serapioni R, The local regularity of solutions of degenerate elliptic equations, Comm. Partial Diff. Equations7 (1982) 77-116. Zbl0498.35042MR643158
  30. [30] Finn R, Serrin J, On the Hölder continuity of quasiconformal and elliptic mappings, Trans. Amer. Math. Soc.89 (1958) 1-15. Zbl0082.29401MR97626
  31. [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. Zbl0891.35039MR1489454
  32. [32] Franchi B, Serapioni R, Serra Cassano F, Irregular solutions of linear degenerate elliptic equations, Potential Analysis9 (1998) 201-216. Zbl0919.35050MR1666899
  33. [33] Giannetti F, Verde A, Variational integrals for elliptic complexes, Studia Math.140 (1) (2000) 79-98. Zbl0968.58019MR1763883
  34. [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. Zbl0855.42009MR1355401
  35. [35] Greco L, Iwaniec T, Sbordone C, Inverting the p-harmonic operator, Manuscripta Math.92 (1997) 249-258. Zbl0869.35037MR1428651
  36. [36] Gustavsson J, Peetre J, Interpolation of Orlicz spaces, Studia Math.LX (1977) 33-59. Zbl0353.46019MR438102
  37. [37] Heinonen J, Koskela P, Sobolev mappings with integrable dilatation, Arch. Rat. Mech. Anal.125 (1993) 81-97. Zbl0792.30016MR1241287
  38. [38] Iwaniec T., Nonlinear Cauchy–Riemann operators in Rn, Trans. AMS, to appear. Zbl1113.35068
  39. [39] Iwaniec T, Koskela P, Martin G, Mappings of BMO-bounded distorsion and Beltrami type operators, Preprint Univ. of Jyväskyla, 1998. 
  40. [40] Iwaniec T, Lutoborski A, Integral estimates for null Lagrangians, Arch. Rat. Mech. Anal.125 (1993) 25-79. Zbl0793.58002MR1241286
  41. [41] Iwaniec T, Martin G, Quasiregular mappings in even dimension, Acta Math.170 (1993) 29-81. Zbl0785.30008MR1208562
  42. [42] Iwaniec T, Martin G, Riesz Transforms and related singular integrals, J. Reine Angew. Math.473 (1996) 25-57. Zbl0847.42015MR1390681
  43. [43] Iwaniec T, Sbordone C, On the integrability of the Jacobian under minimal hypotheses, Arch. Rat. Mech. Anal.119 (1992) 129-143. Zbl0766.46016MR1176362
  44. [44] Iwaniec T, Sbordone C, Riesz transforms and elliptic pde's with VMO coefficients, J. d'Analyse Math.74 (1998) 183-212. Zbl0909.35039MR1631658
  45. [45] Iwaniec T, Sbordone C, Div-curl fields of finite distorsion, C.R. Acad. Sci. Paris, Serie I327 (1998) 729-734. Zbl0916.30015MR1660033
  46. [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. Zbl0963.58003MR1747627
  47. [47] Iwaniec T, Šverák V, On mappings with integrable dilatation, Proc. Amer. Math. Soc.118 (1993) 181-188. Zbl0784.30015MR1160301
  48. [48] Iwaniec T, Verde A, A study of Jacobians in Hardy–Orlicz spaces, Proc. Roy. Soc. Edinburgh29A (1999) 539-570. Zbl0954.46018
  49. [49] John O, Malý J, Stará J, Nowhere continuous solutions to elliptic systems, Comm. Math. Univ. Carolinae30 (1) (1989) 33-43. Zbl0691.35024MR995699
  50. [50] Kilpeläinen T, Malý J, Degenerate elliptic equations with measure data and nonlinear potentials, Ann. Scuola Norm. Sup. Pisa, Ser. IV19 (1992) 591-613. Zbl0797.35052MR1205885
  51. [51] Koskela P, Manfredi J, Villamore E, Regularity theory and traces of A̧-harmonic functions, Trans. Amer. Math. Soc.348 (2) (1996) 755-766. Zbl0849.31015
  52. [52] Krasnosel'skii M.A, Rutickii Yu.B, Convex Functions and Orlicz spaces, P. Noordhoff Ltd, Groningen, 1961, translation. Zbl0095.09103MR126722
  53. [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. Zbl0869.35019MR1432370
  54. [54] Manfredi J, Villamor E, Mappings with integrable dilatation in higher dimensions, Bull. Amer. Math. Soc.32 (1995) 235-240. Zbl0857.30020MR1313107
  55. [55] Meyers N, An Lp-estimate for the gradient of solutions of second order elliptic divergence equations, Ann. Sc. Norm. Sup. Pisa17 (1963) 189-206. Zbl0127.31904MR159110
  56. [56] Migliaccio L., Moscariello G., Higher integrability of Div-Curl Products (1997), Ricerche di Matematica, to appear. MR1795037
  57. [57] Iwaniec T., Migliaccio L., Moscariello G., Passarelli di Napoli A., Integrability Theory of Nonlinear Elliptic Complexes, to appear. 
  58. [58] Modica G, Quasiminimi di alcuni funzionali degeneri, Annali di Matematica (1984) 121-143. Zbl0596.49008
  59. [59] Moscariello G, On the integrability of the Jacobian in Orlicz spaces, Math. Japonica40 (2) (1994) 323-329. Zbl0805.46026MR1297249
  60. [60] Müller S, Higher integrability of determinants and weak convergence in L1, J. Reine Angew. Math.412 (1990) 20-34. Zbl0713.49004MR1078998
  61. [61] Murat F, Equations non linéaires avec second membre L1 on mésure, Preprint, 1994. 
  62. [62] Palagachev D.K, Quasilinear elliptic equations with VMO coefficients, Trans. Amer. Math. Soc.347 (1995) 2481-2493. Zbl0833.35048MR1308019
  63. [63] Rao M.M, Ren Z.D, Theory of Orlicz Spaces, Marcel Dekker, New York, 1991. Zbl0724.46032MR1113700
  64. [64] Ryazanov V, Srebro U, Yakubov E, BMO-quasiconformal mappings, Preprint 155, University of Helsinki, August 1997. MR1828484
  65. [65] Sbordone C, New estimates for div-curl products and very weak solutions of pde's, Ann. Scuola Norm. Sup. Pisa IVXXV (4) (1997) 739-756. Zbl1073.35515MR1655540
  66. [66] Serrin J, Pathological solutions of elliptic differential equations, Ann. Sc. Norm. Sup. Pisa18 (1964) 385-387. Zbl0142.37601MR170094
  67. [67] Souček J, Singular solutions to linear elliptic systems, Comm. Math. Univ. Carolinae25 (1984) 273-281. Zbl0564.35008MR768815
  68. [68] Stampacchia G, Le probléme de Dirichlet pour les equations elliptiques du second ordre a coefficients discontinus, Ann. Inst. Fourier, Grenoble15 (1965) 189-258. Zbl0151.15401MR192177
  69. [69] Stein E, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, 1970. Zbl0207.13501MR290095
  70. [70] Stein E, Harmonic Analysis, Princeton University Press, 1993. Zbl0821.42001MR1232192
  71. [71] Šverák V, Rank-one convexity does not imply quasiconvexity, Proc. Royal Soc. Edinburgh120A (1992) 185-189. Zbl0777.49015MR1149994
  72. [72] Trudinger N, On the regularity of generalized solutions of linear nonuniformly elliptic equations, Arch. Rat. Mech. Anal.42 (1971) 51-62. Zbl0218.35035MR344656
  73. [73] Tukia P, Compactness properties of μ-homeomorphisms, Ann. Acad. Sci., Ser. A1 Math.16 (1991) 47-69. Zbl0692.30017
  74. [74] Vekua I.N., Generalized Analytic Functions, Pure and Applied Mathematics, Vol. 25, Pergamon Press, Oxford. Zbl0100.07603MR108572

Citations in EuDML Documents

top
  1. Flavia Giannetti, Antonia Passarelli di Napoli, On the continuity of degenerate n-harmonic functions
  2. Patrizia Di Gironimo, Quasiharmonic Fields: a Higher Integrability Result
  3. Flavia Giannetti, Antonia Passarelli di Napoli, On the continuity of degenerate -harmonic functions
  4. M. N. Benbourhim, A. Bouhamidi, Meshless Polyharmonic Div-Curl Reconstruction
  5. Flavia Giannetti, Anna Verde, Variational integrals for elliptic complexes
  6. Daniel Faraco, Milton's conjecture on the regularity of solutions to isotropic equations
  7. Flavia Giannetti, Anna Verde, Lower semicontinuity of a class of multiple integrals below the growth exponent
  8. Maria Rosaria Formica, Carlo Sbordone, On the G -convergence of Morrey operators
  9. Claudia Capone, Quasiharmonic fields and Beltrami operators
  10. Aline Bonami, Tadeusz Iwaniec, Peter Jones, Michel Zinsmeister, On the Product of Functions in and 1

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.