Gradient regularity for minimizers of functionals under p - q subquadratic growth

F. Leonetti; E. Mascolo; F. Siepe

Bollettino dell'Unione Matematica Italiana (2001)

  • Volume: 4-B, Issue: 3, page 571-586
  • ISSN: 0392-4041

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Leonetti, F., Mascolo, E., and Siepe, F.. "Gradient regularity for minimizers of functionals under $p$-$q$ subquadratic growth." Bollettino dell'Unione Matematica Italiana 4-B.3 (2001): 571-586. <http://eudml.org/doc/194747>.

@article{Leonetti2001,
author = {Leonetti, F., Mascolo, E., Siepe, F.},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {571-586},
publisher = {Unione Matematica Italiana},
title = {Gradient regularity for minimizers of functionals under $p$-$q$ subquadratic growth},
url = {http://eudml.org/doc/194747},
volume = {4-B},
year = {2001},
}

TY - JOUR
AU - Leonetti, F.
AU - Mascolo, E.
AU - Siepe, F.
TI - Gradient regularity for minimizers of functionals under $p$-$q$ subquadratic growth
JO - Bollettino dell'Unione Matematica Italiana
DA - 2001/10//
PB - Unione Matematica Italiana
VL - 4-B
IS - 3
SP - 571
EP - 586
LA - eng
UR - http://eudml.org/doc/194747
ER -

References

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  2. ACERBI, E.- FUSCO, N., Regularity for minimizers of non-quadratic functionals. The case 1 < p < 2 , Journ. of Math. Anal. and Applications, 140 (1989), 115-135. Zbl0686.49004MR997847
  3. BHATTACHARYA, T.- LEONETTI, F., A new Poincaré inequality and its applications to the regularity of minimizers of integral functionals with nonstandard growth, Nonlinear Analysis TMA, vol. 17, 9 (1991), 833-839. Zbl0779.49046MR1131493
  4. BOCCARDO, L.- MARCELLINI, P.- SBORDONE, C., L -regularity for variational problems with sharp non standard growth conditions, Boll. U.M.I. (7) 4-A (1990), 219-225. Zbl0711.49058MR1066774
  5. CHOE, H. J., Interior behavior of minimizers for certain functionals with non standard growth conditions, Nonlinear Analysis TMA, 19 (1992), 933-945. Zbl0786.35040MR1192273
  6. CIANCHI A., A.- FUSCO, N., Gradient regularity for minimizers under general growth conditions, J. reine angew. Math., 507 (1999), 15-36. Zbl0913.49024MR1670258
  7. DALL'AGLIO, A.- MASCOLO, E., Regularity for a class of non linear elliptic systems with non standard growth conditions, To appear. 
  8. ESPOSITO, L.- LEONETTI, F.- MINGIONE, G., Regularity for minimizers of functionals with p - q growth, NoDEA Nonlinear Differential Equations Appl., 6 (1999), 133-148. Zbl0928.35044MR1694803
  9. ESPOSITO, L.- LEONETTI, F.- MINGIONE, G., Higher integrability for minimizers of integral functionals with p , q growth, J. Differential Equations, 157 (1999), 414-438. Zbl0939.49021MR1713266
  10. FUSCO, N.- SBORDONE, C., Higher integrability of the gradient of minimizers of functionals with nonstandard growth conditions, Comm. on Pure and Appl. Math., 43 (1990), 673-683. Zbl0727.49021MR1057235
  11. GIAQUINTA, M., Multiple integrals in the calculus of variations and non linear elliptic systems, Annals of Math. Studies, 105 (1983), Princeton Univ. Press. Zbl0516.49003MR717034
  12. GIAQUINTA, M., Growth conditions and regularity, a counterexample, Manuscripta Math., 59 (1987), 245-248. Zbl0638.49005MR905200
  13. GIUSTI, E., Metodi diretti nel calcolo delle variazioni, U.M.I. (1994). MR1707291
  14. HONG, M. C., Some remarks on the minimizers of variational integrals with non standard growth conditions, Boll. U.M.I., 6-A (1992), 91-101. Zbl0768.49022MR1164739
  15. LIEBERMAN, G., The natural generalization of the natural growth conditions of Ladyzhenskaya and Ural'tseva for elliptic equations, Comm. Partial Differential Equations, 16 (1991), 311-361. Zbl0742.35028MR1104103
  16. MARCELLINI, P., Un example de solution discontinue d'un probléme variationel dans le cas scalaire, Preprint Ist. «U. Dini», Firenze (1987). 
  17. MARCELLINI, P., Regularity of minimizers of integrals in the calculus of variations with non standard growth conditions, Arch. Rat. Mech. and Analysis, 105 (1989), 267-284. Zbl0667.49032MR969900
  18. MARCELLINI, P., Regularity and existence of solutions of elliptic equations with p , q -growth conditions, J. Diff. Equat., 90 (1991), 1-30. Zbl0724.35043MR1094446
  19. MARCELLINI, P., Everywhere regularity for a class of elliptic systems without growth conditions, Ann. Scuola Norm. Sup. Pisa, Cl. sci., 23 (1996), 1-25. Zbl0922.35031MR1401415

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