On weakly A-harmonic tensors

Bianca Stroffolini

Studia Mathematica (1995)

  • Volume: 114, Issue: 3, page 289-301
  • ISSN: 0039-3223

Abstract

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We study very weak solutions of an A-harmonic equation to show that they are in fact the usual solutions.

How to cite

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Stroffolini, Bianca. "On weakly A-harmonic tensors." Studia Mathematica 114.3 (1995): 289-301. <http://eudml.org/doc/216193>.

@article{Stroffolini1995,
abstract = {We study very weak solutions of an A-harmonic equation to show that they are in fact the usual solutions.},
author = {Stroffolini, Bianca},
journal = {Studia Mathematica},
keywords = {-harmonic equation; Hodge decompositions; commutator estimates},
language = {eng},
number = {3},
pages = {289-301},
title = {On weakly A-harmonic tensors},
url = {http://eudml.org/doc/216193},
volume = {114},
year = {1995},
}

TY - JOUR
AU - Stroffolini, Bianca
TI - On weakly A-harmonic tensors
JO - Studia Mathematica
PY - 1995
VL - 114
IS - 3
SP - 289
EP - 301
AB - We study very weak solutions of an A-harmonic equation to show that they are in fact the usual solutions.
LA - eng
KW - -harmonic equation; Hodge decompositions; commutator estimates
UR - http://eudml.org/doc/216193
ER -

References

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  1. [B] J. M. Ball, Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal. 63 (1977), 337-403. Zbl0368.73040
  2. [BCO] J. M. Ball, J. C. Curie and P. J. Olver, Null Lagrangians, weak continuity, and variational problems of arbitrary order, J. Funct. Anal. 41 (1981), 135-174. 
  3. [BG1] L. Boccardo and D. Giachetti, Alcune osservazioni sulla regolarità delle soluzioni di problemi fortemente non lineari e applicazioni, Ricerche Mat. 34 (1985), 309-323. 
  4. [BG2] L. Boccardo and D. Giachetti, Existence results via regularity for some nonlinear elliptic problems, Comm. Partial Differential Equations 14 (1989), 663-680. Zbl0678.35035
  5. [BMS] L. Boccardo, P. Marcellini and C. Sbordone, L -regularity for variational problems with sharp non standard growth conditions, Boll. Un. Mat. Ital. A (7) 4 (1990), 219-226. Zbl0711.49058
  6. [BI] B. Bojarski and T. Iwaniec, Analytical foundations of the theory of quasiconformal mappings in R n , Ann. Acad. Sci. Fenn. Ser. AI 8 (1983), 257-324. Zbl0548.30016
  7. [C] H. Cartan, Differential Forms, Houghton Mifflin, Boston, 1970. Zbl0213.37001
  8. [CLMS] R. Coifman, P. L. Lions, Y. Meyer et S. Semmes, Compacité par compensation et espaces de Hardy, C. R. Acad. Sci. Paris 309 (1989), 945-949. Zbl0684.46044
  9. [EM] A. Elcrat and N. G. Meyers, Some results on regularity for solutions of nonlinear elliptic systems and quasiregular functions, Duke Math. J. 42 (1975), 121-136. Zbl0347.35039
  10. [G] F. W. Gehring, The L p -integrability of the partial derivatives of a quasiconformal mapping, Acta Math. 130 (1973), 265-277. Zbl0258.30021
  11. [Gi] M. Giaquinta, Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems, Ann. of Math. Stud. 105, Princeton Univ. Press, 1983. 
  12. [GM] M. Giaquinta and L. Modica, Regularity results for some classes of higher order nonlinear elliptic systems, J. Reine Angew. Math. 311/312 (1979), 145-169. Zbl0409.35015
  13. [H] W. V. D. Hodge, A Dirichlet problem for harmonic functionals, Proc. London Math. Soc. 2 (1933), 257-303. Zbl0008.02203
  14. [I1] T. Iwaniec, Projections onto gradient fields and L p -estimates for degenerate elliptic operators, Studia Math. 75 (1983), 293-312. Zbl0552.35034
  15. [I2] T. Iwaniec, p-harmonic tensors and quasiregular mappings, Ann. of Math. 136 (1992), 589-624. 
  16. [I3] T. Iwaniec, L p -theory of quasiregular mappings, in: Lecture Notes in Math. 1508, Springer, 1992, 39-64. 
  17. [IL] T. Iwaniec and A. Lutoborski, Integral estimates for null Lagrangians, Arch. Rational Mech. Anal. 125 (1993), 25-79. Zbl0793.58002
  18. [IM1] T. Iwaniec and G. Martin, Quasiregular mappings in even dimensions, Acta Math. 170 (1993), 29-81. Zbl0785.30008
  19. [IM2] T. Iwaniec and G. Martin, The Beurling-Ahlfors transform in n and related singular integrals, preprint, I.H.E.S., August 1990. 
  20. [IMNS] T. Iwaniec, L. Migliaccio, L. Nania and C. Sbordone, Integrability and removability results for quasiregular mappings in high dimension, Math. Scand., to appear. Zbl0824.30009
  21. [IS] T. Iwaniec and C. Sbordone, Weak minima of variational integrals, J. Reine Angew. Math. 454 (1994), 143-161. Zbl0802.35016
  22. [JRW] B. Jawerth, R. Rochberg and G. Weiss, Commutator and other second order estimates in real interpolation theory, Ark. Mat. 24 (1986), 191-219. Zbl0655.41005
  23. [L] J. L. Lewis, On very weak solutions of certain elliptic and parabolic systems, Comm. Partial Differential Equations 18 (1993), 1515-1537. Zbl0796.35061
  24. [Me] N. Meyers, An L p -estimate for the gradient of solutions of second order elliptic divergence equations, Ann. Scuola Norm. Sup. Pisa 17 (1963), 189-206. Zbl0127.31904
  25. [M1] M. Milman, A commutator theorem with applications, in: Proc. Conf. on Function Spaces, Poznań, 1992, Kluwer, to appear. 
  26. [M2] M. Milman, Integrability of the Jacobian of orientation preserving maps: interpolation techniques, C. R. Acad. Sci. Paris 317 (1993), 539-543. Zbl0789.46035
  27. [MS] M. Milman and T. Schonbeck, Second order estimates in interpolation theory and applications, Proc. Amer. Math. Soc. 110 (1990), 961-969. 
  28. [R] R. Rochberg, Higher order estimates in complex interpolation theory, preprint. Zbl0866.46047
  29. [RW] R. Rochberg and G. Weiss, Derivatives of analytic families of Banach spaces, Ann. of Math. 118 (1983), 315-347. Zbl0539.46049
  30. [SS] L. M. Sibner and R. B. Sibner, A nonlinear Hodge de Rham theorem, Acta Math. 125 (1970), 57-73. 
  31. [S] G. Stampacchia, Equations elliptiques du second ordre à coefficients discontinus, Sém. Math. Sup. 16, Les Presses de l'Université de Montréal, Montréal, 1966. Zbl0151.15501
  32. [St] B. Stroffolini, Global boundedness of solutions of anisotropic variational problems, Boll. Un. Mat. Ital. A (7) 5 (1991), 345-352. Zbl0754.49026
  33. [U] K. Uhlenbeck, Regularity for a class of nonlinear elliptic systems, Acta Math. 138 (1977), 219-250. Zbl0372.35030

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