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.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

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 $p(x)>1$.
In questo lavoro si provano risultati di regolarità per minimi di funzionali scalari $\int f (x, u, Du)$ 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. 
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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/

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