Hölder continuity results for a class of functionals with non-standard growth

Eleuteri, Michela

Bollettino dell'Unione Matematica Italiana, Tome 7-A (2004), p. 129-157 / Harvested from Biblioteca Digitale Italiana di Matematica

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Abstract
Résumé

We prove regularity results for real valued minimizers of the integral functional $\int f (x, u, D u)$ under non-standard growth conditions of $p (x)$ -type, i.e. $L^{- 1} {|z|}^{p (x)} \leq f (x, s, z) \leq L (1 + {|z|}^{p (x)})$ under sharp assumptions on the continuous function $p (x) > 1$ .

In questo lavoro si provano risultati di regolarità per minimi di funzionali scalari $\int f (x, u, D u)$ a crescita non-standard di tipo $p (x)$ , cioè: $L^{- 1} {|z|}^{p (x)} \leq f (x, s, z) \leq L (1 + {|z|}^{p (x)}) .$ Si considerano per la funzione esponente $p (x) > 1$ ipotesi di regolarità ottimali.

Publié le : 2004-02-01

MR 2044264 | Zbl 1178.49045

@article{BUMI_2004_8_7B_1_129_0,
     author = {Michela Eleuteri},
     title = {H\"older continuity results for a class of functionals with non-standard growth},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {7-A},
     year = {2004},
     pages = {129-157},
     zbl = {1178.49045},
     mrnumber = {2044264},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2004_8_7B_1_129_0}
}

Eleuteri, Michela. Hölder continuity results for a class of functionals with non-standard growth. Bollettino dell'Unione Matematica Italiana, Tome 7-A (2004) pp. 129-157. http://gdmltest.u-ga.fr/item/BUMI_2004_8_7B_1_129_0/

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