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

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.