, Volume 126, Issue 1, pp 1-40

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

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Abstract

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.