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For higher order functionals $$\int_\Omega f(x, \delta u(x), {D^m}u(x))\,dx$$ with p(x)-growth with respect to the variable containing 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.

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