## Abstract

Let O ? R^{n} be a bounded domain and F: double struct M sign ? R a given strongly quasiconvex integrand of class C^{2} satisfying the growth condition |F(?)| ? c(l + |?|^{p}) for some c > 0 and 2? p < 8. Consider the multiple integral I[u] = ?_{O} F(?u) where u ? W^{1, p}(O, R^{N}). The main result of the paper is the proof that any strong local minimizer of I[·] is of class C _{loc}^{1,a} for any a ? (0,1) on an open set of full n-dimensional measure. In the case of weak local minimizers we establish the same result under the extra assumption that the oscillations in the gradient of the minimizer are not too large. Without such an assumption weak local minimizers need not be partially regular as we show by a class of examples. We also briefly discuss the question of existence of strong local minimizers for I[·] and connections of our results to extensions of Weierstrass' sufficiency theorem to the multi-dimensional setting.

Original language | English |
---|---|

Pages (from-to) | 63-89 |

Number of pages | 27 |

Journal | Archive for Rational Mechanics and Analysis |

Volume | 170 |

Issue number | 1 |

DOIs | |

Publication status | Published - Nov 2003 |