Functionals with growth and regularity
Emilio Acerbi; Giuseppe Mingione
- Volume: 11, Issue: 3, page 169-174
- ISSN: 1120-6330
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topAcerbi, Emilio, and Mingione, Giuseppe. "Functionals with $p(x)$ growth and regularity." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 11.3 (2000): 169-174. <http://eudml.org/doc/252312>.
@article{Acerbi2000,
abstract = {We consider the integral functional $\int f(x,Du) dx$ under non standard growth assumptions of $(p,q)$-type: namely, we assume that $|z|^\{p(x)\} \le f(x,z) \le L(1 + |z|^\{p(x)\})$, a relevant model case being the functional $\int |Du|^\{p(x)\} dx$. Under sharp assumptions on the continuous function $p(x) > 1$ we prove regularity of minimizers both in the scalar and in the vectorial case, in which we allow for quasiconvex energy densities. Energies exhibiting this growth appear in several models from mathematical physics.},
author = {Acerbi, Emilio, Mingione, Giuseppe},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Integral functionals; Minimizers; Nonstandard growth; Partial regularity; integral functionals; minimizers; partial regularity},
language = {eng},
month = {9},
number = {3},
pages = {169-174},
publisher = {Accademia Nazionale dei Lincei},
title = {Functionals with $p(x)$ growth and regularity},
url = {http://eudml.org/doc/252312},
volume = {11},
year = {2000},
}
TY - JOUR
AU - Acerbi, Emilio
AU - Mingione, Giuseppe
TI - Functionals with $p(x)$ growth and regularity
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2000/9//
PB - Accademia Nazionale dei Lincei
VL - 11
IS - 3
SP - 169
EP - 174
AB - We consider the integral functional $\int f(x,Du) dx$ under non standard growth assumptions of $(p,q)$-type: namely, we assume that $|z|^{p(x)} \le f(x,z) \le L(1 + |z|^{p(x)})$, a relevant model case being the functional $\int |Du|^{p(x)} dx$. Under sharp assumptions on the continuous function $p(x) > 1$ we prove regularity of minimizers both in the scalar and in the vectorial case, in which we allow for quasiconvex energy densities. Energies exhibiting this growth appear in several models from mathematical physics.
LA - eng
KW - Integral functionals; Minimizers; Nonstandard growth; Partial regularity; integral functionals; minimizers; partial regularity
UR - http://eudml.org/doc/252312
ER -
References
top- Acerbi, E. - Mingione, G., Regularity results for a class of functionals with nonstandard growth. Arch. Rational Mech. Anal., to appear. Zbl0984.49020
- Acerbi, E. - Mingione, G., Regularity for a class of quasiconvex functionals with nonstandard growth. To appear. Zbl1027.49031
- Alkhutov, Yu. A., The Harnack inequality and the Hölder property of solutions of nonlinear elliptic equations with a nonstandard growth condition. Differential Equations, 33, 1997, 1653-1663. Zbl0949.35048MR1669915
- Coscia, A. - Mingione, G., Hölder continuity of the gradient of -harmonic mappings. C. R. Acad. Sci. Paris, 328, 1999, 363-368. Zbl0920.49020MR1675954DOI10.1016/S0764-4442(99)80226-2
- Fan, Xiangling - Zhao, Dun, A class of De Giorgi type and Hölder continuity. Nonlinear Anal. T.M.A., 36 A, 1999, 295-318. Zbl0927.46022MR1688232DOI10.1016/S0362-546X(97)00628-7
- Marcellini, P., Regularity for some scalar variational problems under general growth conditions. J. Optim. Theory Appl., 90, 1996, 161-181. Zbl0901.49030MR1397651DOI10.1007/BF02192251
- Zhikov, V.V., On some variational problems. Russian J. Math. Physics, 5, 1997, 105-116. Zbl0917.49006MR1486765
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