On interior regularity of minimizers of p(x)p(x)-energy functionals

The aim of the paper is to obtain everywhere C1,αC1,α-regularity in the interior for a minimizer of the p(x)p(x)-energy functional E(v;Ω)=∫Ω(gαβ(x)hij(v)Dαvi(x)Dβvj(x))p(x)/2dx,E(v;Ω)=∫Ω(gαβ(x)hij(v)Dαvi(x)Dβvj(x))p(x)/2dx, defined for maps v:Ω(⊂Rm)→Rnv:Ω(⊂Rm)→Rn, under the so-called one-sided condition, supposing the Lipschitz continuity assumption on the exponent p(x)≥2p(x)≥2.