Geodesic
Hölder continuity results for a class of functionals with non-standard growth
Bollettino della Unione matematica italiana, Série 8, 7B (2004) no. 1, pp. 129-157

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We prove regularity results for real valued minimizers of the integral functional $\int f (x, u, Du)$ 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 $p(x)>1$. 
@article{BUMI_2004_8_7B_1_a5,
     author = {Eleuteri, Michela},
     title = {H\"older continuity results for a class of functionals with non-standard growth},
     journal = {Bollettino della Unione matematica italiana},
     pages = {129--157},
     publisher = {mathdoc},
     volume = {Ser. 8, 7B},
     number = {1},
     year = {2004},
     zbl = {1178.49045},
     mrnumber = {MR2044264},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2004_8_7B_1_a5/}
}
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Eleuteri, Michela. Hölder continuity results for a class of functionals with non-standard growth. Bollettino della Unione matematica italiana, Série 8, 7B (2004) no. 1, pp. 129-157. http://geodesic.mathdoc.fr/item/BUMI_2004_8_7B_1_a5/