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Partial regularity of minimizers of higher order integrals with (p, q)-growth
Published online by Cambridge University Press: 23 April 2010
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 $f:{\textstyle \bigodot^m}(\R^{n},\R^{N})\to\mathbb{R}$
,
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 the
functional $F[\cdot]$
and prove a partial $C^{m,\alpha}_{\rm loc}$
-regularity result.
- Type
- Research Article
- Information
- ESAIM: Control, Optimisation and Calculus of Variations , Volume 17 , Issue 2 , April 2011 , pp. 472 - 492
- Copyright
- © EDP Sciences, SMAI, 2010
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