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 ${\Omega }_0\subset \Omega$ of full Lebesgue- measure, provided that the exponent function $p:\Omega \to (1,\infty )$ itself is Hölder continuous.

29 pages