Local boundedness for minimizers of variational integrals under anisotropic nonstandard growth conditions

Zesheng Feng; Aiping Zhang; Hongya Gao

Czechoslovak Mathematical Journal (2024)

  • Volume: 74, Issue: 4, page 1165-1184
  • ISSN: 0011-4642

Abstract

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This paper deals with local boundedness for minimizers of vectorial integrals under anisotropic growth conditions by using De Giorgi’s iterative method. We consider integral functionals with the first part of the integrand satisfying anisotropic growth conditions including a convex nondecreasing function g , and with the second part, a convex lower order term or a polyconvex lower order term. Local boundedness of minimizers is derived.

How to cite

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Feng, Zesheng, Zhang, Aiping, and Gao, Hongya. "Local boundedness for minimizers of variational integrals under anisotropic nonstandard growth conditions." Czechoslovak Mathematical Journal 74.4 (2024): 1165-1184. <http://eudml.org/doc/299614>.

@article{Feng2024,
abstract = {This paper deals with local boundedness for minimizers of vectorial integrals under anisotropic growth conditions by using De Giorgi’s iterative method. We consider integral functionals with the first part of the integrand satisfying anisotropic growth conditions including a convex nondecreasing function $g$, and with the second part, a convex lower order term or a polyconvex lower order term. Local boundedness of minimizers is derived.},
author = {Feng, Zesheng, Zhang, Aiping, Gao, Hongya},
journal = {Czechoslovak Mathematical Journal},
keywords = {local boundedness; minimizer; variational integral; anisotropic growth; convex; polyconvex},
language = {eng},
number = {4},
pages = {1165-1184},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Local boundedness for minimizers of variational integrals under anisotropic nonstandard growth conditions},
url = {http://eudml.org/doc/299614},
volume = {74},
year = {2024},
}

TY - JOUR
AU - Feng, Zesheng
AU - Zhang, Aiping
AU - Gao, Hongya
TI - Local boundedness for minimizers of variational integrals under anisotropic nonstandard growth conditions
JO - Czechoslovak Mathematical Journal
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 74
IS - 4
SP - 1165
EP - 1184
AB - This paper deals with local boundedness for minimizers of vectorial integrals under anisotropic growth conditions by using De Giorgi’s iterative method. We consider integral functionals with the first part of the integrand satisfying anisotropic growth conditions including a convex nondecreasing function $g$, and with the second part, a convex lower order term or a polyconvex lower order term. Local boundedness of minimizers is derived.
LA - eng
KW - local boundedness; minimizer; variational integral; anisotropic growth; convex; polyconvex
UR - http://eudml.org/doc/299614
ER -

References

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  1. Acerbi, E., Fusco, N., 10.1006/jdeq.1994.1002, J. Differ. Equations 107 (1994), 46-67. (1994) Zbl0807.49010MR1260848DOI10.1006/jdeq.1994.1002
  2. Cupini, G., Focardi, M., Leonetti, F., Mascolo, E., 10.1515/anona-2020-0039, Adv. Nonlinear Anal. 9 (2020), 1008-1025. (2020) Zbl1429.49042MR3998218DOI10.1515/anona-2020-0039
  3. Cupini, G., Leonetti, F., Mascolo, E., 10.1007/s00205-017-1074-7, Arch. Ration. Mech. Anal. 224 (2017), 269-289. (2017) Zbl1365.49035MR3609252DOI10.1007/s00205-017-1074-7
  4. Cupini, G., Marcellini, P., Mascolo, E., 10.3934/dcdsb.2009.11.67, Discrete Contin. Dyn. Syst., Ser. B 11 (2009), 67-86. (2009) Zbl1158.49040MR2461809DOI10.3934/dcdsb.2009.11.67
  5. Cupini, G., Marcellini, P., Mascolo, E., 10.1007/s10957-015-0722-z, J. Optim. Theory Appl. 166 (2015), 1-22. (2015) Zbl1325.49043MR3366102DOI10.1007/s10957-015-0722-z
  6. Cupini, G., Marcellini, P., Mascolo, E., 10.1016/j.na.2016.06.002, Nonlinear Anal., Theory Methods Appl., Ser. A 153 (2017), 294-310. (2017) Zbl1358.49032MR3614673DOI10.1016/j.na.2016.06.002
  7. Fusco, N., Sbordone, C., 10.1007/BF02567909, Manuscr. Math. 69 (1990), 19-25. (1990) Zbl0722.49012MR1070292DOI10.1007/BF02567909
  8. Giusti, E., 10.1142/5002, World Scientific, Singapore (2003). (2003) Zbl1028.49001MR1962933DOI10.1142/5002
  9. Granucci, T., Randolfi, M., 10.1007/s00229-021-01360-0, Manuscr. Math. 170 (2023), 677-772. (2023) Zbl1512.49038MR4548604DOI10.1007/s00229-021-01360-0
  10. Han, Y., Fang, M., Xia, L., Gao, H., 10.48550/arXiv.2402.09455, Available at https://arxiv.org/abs/2402.09455 (2024), 26 pages. (2024) DOI10.48550/arXiv.2402.09455
  11. Leonetti, F., Petricca, P. V., 10.1016/j.na.2015.09.009, Nonlinear Anal., Theory Methods Appl., Ser. A 129 (2015), 258-264. (2015) Zbl1327.49064MR3414930DOI10.1016/j.na.2015.09.009
  12. Marcellini, P., 10.1007/BF00251503, Arch. Ration. Mech. Anal. 105 (1989), 267-284. (1989) Zbl0667.49032MR0969900DOI10.1007/BF00251503
  13. Marcellini, P., 10.1016/0022-0396(91)90158-6, J. Differ. Equations 90 (1991), 1-30. (1991) Zbl0724.35043MR1094446DOI10.1016/0022-0396(91)90158-6
  14. Troisi, M., Teoremi di inclusione per spazi di Sobolev non isotropi, Ric. Mat. 18 (1969), 3-24 Italian. (1969) Zbl0182.16802MR0415302

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