1 results
Partial regularity of minimizers of higher order integrals with (p, q)-growth
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- Journal:
- ESAIM: Control, Optimisation and Calculus of Variations / Volume 17 / Issue 2 / April 2011
- Published online by Cambridge University Press:
- 23 April 2010, pp. 472-492
- Print publication:
- April 2011
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- Article
- Export citation
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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 $f:{\textstyle \bigodot^m}(\R^{n},\R^{N})\to\mathbb{R}$
, m ≥ 1 is strictly quasiconvex and satisfies a non-standard growth condition.More precisely we assume that f fulfills the (p, q)-growth condition\[\gamma|A|^p\le f(A)\le L(1+|A|^q)\qquad \mbox{for all }A \in {\textstyle \bigodot^m}(\R^{n},\R^{N}),\]
with γ, L > 0 and $1< p \le q<\min\big\{p+\frac1n,\frac{2n-1}{2n-2}p\big\}$
. We study minimizers of thefunctional $F[\cdot]$
and prove a partial $C^{m,\alpha}_{\rm loc}$
-regularity result.
