Weak minima of variational integrals

Journal fur die Reine und Angewandte Mathematik

Volumn 1994, Issue 454, 1994, Pages 143-162

  Iwaniec, T ^a,b   Sbordone, C ^a,b  

^a SYRACUSE UNIVERSITY   (United States)

^b University of Naples   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84941379416     PISSN: 00754102     EISSN: 14355345     Source Type: Journal    
DOI: 10.1515/crll.1994.454.143     Document Type: Article

References (26)

1. J. Berg and J. Lefstrom Interpolation Spaces, Springer 1976.
2. L. Boccardo, An Ls-Estimate for the Gradient of Solutions of Some Nonlinear Unilateral Problems, Ann. Mat. pura appl. (IV) CXLI (1985), 277–287.
3. B. Bojarski and T. Iwaniec, Analytical foundations of the theory of quasi-conformal mappings in Rn, Ann. Acad. Sci. Fenn. (A.I.) 8 (1983), 257–324.
4. F. Browder, Nonlinear elliptic boundary value problems, Bull. Amer. Math. Soc. 69 (1963), 862–874.
5. M. Cwikel B. Jawerth, M. Milman and R. Rochberg, Differential estimates and commutators in interpolation theory, Analysis at Urbana II, London Math. Soc., Cambridge Univ. Press, (1989), 170–220.
6. N. Fusco and C. Sbordone, Higher integrability of the Gradient of Minimizers of Functionals with Nonstandard Growth Conditions, Comm. Pure Appl. Math. XLIII (1990), 673–680.
7. F. W. Gehring, The Lp-integrability of the partial derivatives of a quasiconformal mapping, Acta Math. 130 (1973), 265–277.
8. D. Giachetti, F. Leonetti and R. Schianchi, On the regularity of very weak minima, to appear.
9. M. Giaquinta, Multiple integrals in the Calculus of Variations and nonlinear elliptic systems, Ann. Math. Stud. 105, Princeton Univ. Press, 1983.
10. M. Giaquinta and G. Modica, Regularity results for some classes of higher order nonlinear elliptic systems, J. reine angew. Math. 311 / 312 (1979), 145–169.
11. L.Greco, T. Iwaniec and G. Moscariello, Limits of the Improved Integrability of the Volume Forms, preprint University of Naples, 1993.
12. T. Iwaniec, Projections onto gradient fields and LP-estimate for degenerated elliptic operators, Stud. Math. 75 (1983), 293–312.
13. T. Iwaniec, p-harmonic tensors and quasiregular mappings, Ann. Math. 136 (1992), 589–624.
14. T. Iwaniec and A. Lutoborski, Integral estimates for null Lagrangians, Arch. Rat. Mech. Anal. 125 (1993), 25–79.
15. T. Iwaniec and G. Martin, Quasiregular mappings in even dimensions, Acta Math. 170 (1993), 29–81.
16. T. Iwaniec and G. Martin, The Beurling-Ahlfors transform in Rnand related singular integrals, Preprint of Inst. Hautes Etudes Sci., 1990.
17. T. Iwaniec, L. Migliaccio, L. Nania and C. Sbordone, Integrability and removability results for quasiregular mappings in high dimensions, Math. Scand., to appear.
18. B. Jawerth, R. Rochberg and G. Weiss, Commutators and other second order estimates in real interpolation theory, Ark. Mat. 24 (1986), 191–219.
19. J. Leray and J. L. Lions, Quelques resultats de Visik sur les problemes elliptiques non lineaires par les methodes de Minty-Browder, Bull. Soc. Math. France 93 (1965), 97–107.
20. J. Lewis, On very weak solutions of certain elliptic systems, Comm. Part. Diff. Equ. 18 (9&10) (1993), 1515–1537.
21. P. Marcellini, On the definition and the lower semicontinuity of certain quasiconvex integrals, Ann. Inst. Henri Poincare 3 (5) (1986), 391–409.
22. N. Meyers, An LP-estimate for the gradient of solutions of second order elliptic divergence equations, Ann. Sc. Norm. Sup. Pisa 17 (1963), 189–206.
23. N. Meyers and A. Elcrat, Some results on regularity for solutions of nonlinear elliptic systems and quasiregular functions, Duke Math. J. 42 (1) (1975), 121–136.
24. M. Milman, A commutator Theorem with Applications, preprint Institute for Advanced Study, 1992.
25. R. Rochberg and G. Weiss, Derivatives of Analytic families of Banach spaces, Ann. Math. 118 (1983), 315–347.
26. E. W. Stredulinski, Higher integrability from reverse Holder inequalities, Indiana Univ. Math. J. 29, 3 (1980), 408–417.