Some remarks on the regularity of minimizers of integrals with anisotropic growth

Tilak Bhattacharya; Francesco Leonetti

Commentationes Mathematicae Universitatis Carolinae (1993)

  • Volume: 34, Issue: 4, page 597-611
  • ISSN: 0010-2628

Abstract

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We prove higher integrability for minimizers of some integrals of the calculus of variations; such an improved integrability allows us to get existence of weak second derivatives.

How to cite

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Bhattacharya, Tilak, and Leonetti, Francesco. "Some remarks on the regularity of minimizers of integrals with anisotropic growth." Commentationes Mathematicae Universitatis Carolinae 34.4 (1993): 597-611. <http://eudml.org/doc/247498>.

@article{Bhattacharya1993,
abstract = {We prove higher integrability for minimizers of some integrals of the calculus of variations; such an improved integrability allows us to get existence of weak second derivatives.},
author = {Bhattacharya, Tilak, Leonetti, Francesco},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {regularity; minimizers; integral functionals; anisotropic growth; anisotropic growth; higher integrability; minimizers; integrals of the calculus of variations},
language = {eng},
number = {4},
pages = {597-611},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Some remarks on the regularity of minimizers of integrals with anisotropic growth},
url = {http://eudml.org/doc/247498},
volume = {34},
year = {1993},
}

TY - JOUR
AU - Bhattacharya, Tilak
AU - Leonetti, Francesco
TI - Some remarks on the regularity of minimizers of integrals with anisotropic growth
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1993
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 34
IS - 4
SP - 597
EP - 611
AB - We prove higher integrability for minimizers of some integrals of the calculus of variations; such an improved integrability allows us to get existence of weak second derivatives.
LA - eng
KW - regularity; minimizers; integral functionals; anisotropic growth; anisotropic growth; higher integrability; minimizers; integrals of the calculus of variations
UR - http://eudml.org/doc/247498
ER -

References

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  1. Acerbi E., Fusco N., Partial regularity under anisotropic ( p , q ) growth conditions, J. Differential Equations, to appear. Zbl0807.49010MR1260848
  2. Acerbi E., Fusco N., Regularity for minimizers of non-quadratic functionals: the case 1 < p < 2 , J. Math. Anal. Appl. 140 (1989), 115-135. (1989) Zbl0686.49004MR0997847
  3. Adams R.A., Sobolev Spaces, New York, 1975. Zbl1098.46001MR0450957
  4. Bhattacharya T., Leonetti F., W 2 , 2 regularity for weak solutions of elliptic systems with nonstandard growth, J. Math. Anal. Appl. 176 (1993), 224-234. (1993) MR1222166
  5. Campanato S., Sistemi ellittici in forma divergenza. Regolarità all'interno., Pisa, 1980. Zbl0453.35026MR0668196
  6. Campanato S., Cannarsa P., Differentiability and partial Hölder continuity of the solutions of nonlinear elliptic systems of order 2 m with quadratic growth, Ann. Scuola Norm. Sup. Pisa 8 (1981), 285-309. (1981) MR0623938
  7. Campanato S., Hölder continuity of the solutions of some nonlinear elliptic systems, Adv. in Math. 48 (1983), 16-43. (1983) Zbl0519.35027MR0697613
  8. Fusco N., Sbordone C., Local boundedness of minimizers in a limit case, Manuscripta Math. 69 (1990), 19-25. (1990) Zbl0722.49012MR1070292
  9. Fusco N., Sbordone C., Some remarks on the regularity of minima of anisotropic integrals, Comm. P.D.E. 18 (1993), 153-167. (1993) Zbl0795.49025MR1211728
  10. Giaquinta M., Growth conditions and regularity, a counterexample, Manuscripta Math. 59 (1987), 245-248. (1987) Zbl0638.49005MR0905200
  11. Giaquinta M., Multiple integrals in the calculus of variations and nonlinear elliptic systems, Princeton, 1983. Zbl0516.49003MR0717034
  12. Leonetti F., Weak differentiability for solutions to nonlinear elliptic systems with p,q-growth conditions, Ann. Mat. Pura Appl. 162 (1992), 349-366. (1992) Zbl0801.35023MR1199662
  13. Leonetti F., Higher integrability for minimizers of integral functionals with nonstandard growth, J. Differential Equations, to appear. Zbl0813.49030MR1293473
  14. Marcellini P., Regularity of minimizers of integrals of the calculus of variations with nonstandard growth conditions, Arch. Rational Mech. Anal. 105 (1989), 267-284. (1989) MR0969900
  15. Marcellini P., Un example de solution discontinue d'un problème variationnel dans ce cas scalaire, preprint Istituto Matematico ``U. Dini'' Universita' di Firenze, 1987/88, n.11. 
  16. Troisi M., Teoremi di inclusione per spazi di Sobolev non isotropi, Ricerche di Mat. 18 (1969), 3-24. (1969) Zbl0182.16802MR0415302

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