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Partial regularity for minima of higher order functionals with p(x) growth

Jens Habermann
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Abstract

For higher order integral functionals with $p(x)$ growth with respect to the highest order derivative $D^m u$, we prove that $D^m u$ is Hölder continuous on an open subset $Ω_0 \subset Ω$ of full Lebesgue- measure, provided that the exponent function $p:Ω\to (1,\infty)$ itself is Hölder continuous.

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Jens Habermann. 2006-10-04. Partial regularity for minima of higher order functionals with p(x) growth. https://arxiv.org/abs/math/0610145

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