| Abstract
| - We consider higher order functionals of the form. $F[u]=\int\limits_\Omega f(D^mu)\,{\rm d}x \qquad\text{for }u:\mathbb{R}^n\supset\Omega\to\mathbb{R}^N,$. where the integrand , m≥ 1 is strictly quasiconvex and satisfies a non-standard growth condition. More precisely we assume that f fulfills the ( p, q)-growth condition . with γ, L> 0 and $1< p \le q<\min\big\{p+\frac1n,\frac{2n-1}{2n-2}p\big\}$. We study minimizers of the functional $F[\cdot]$ and prove a partial $C^{m,\alpha}_{\rm loc}$-regularity result.
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