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

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

2006-10-04

arxiv.org/abs/math/0610145v1

Mathematics

Analysis of PDEs

29 pages

Scientific paper

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 H\"older 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 H\"older
continuous.

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