Calculus of Variations and Geometric Measure Theory
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M. Eleuteri

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

created by eleuteri on 15 Oct 2009


Published Paper

Inserted: 15 oct 2009

Journal: Boll. Unione Mat. Ital.
Volume: (8)
Number: 7 - B
Pages: 129-157
Year: 2004


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. $$ L{-1}
{p(x)}\leq f(x,s,z) \leq L(1+
{p(x)}) $$ under sharp assumptions on the continuous function $p(x) >1.$

Keywords: Non standard growth, Hölder continuity


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