### Abstract

We study all the possible weak limits of a minimizing sequence, for p-energy functionals, consisting of continuous maps between Riemannian manifolds subject to a Dirichlet boundary condition or a homotopy condition. We show that if p is not an integer, then any such weak limit is a strong limit and, in particular, a stationary p-harmonic map which is C^{1,α} continuous away from a closed subset of the Hausdorff dimension ≤ n - [p] - 1. If p is an integer, then any such weak limit is a weakly p-harmonic map along with a (n - p)-rectifiable Radon measure μ. Moreover, the limiting map is C^{1,α} continuous away from a closed subset Σ = spt μ ∪ S with H^{n-p}(S) = 0. Finally, we discuss the possible varifolds type theory for Sobolev mappings.

Original language | English (US) |
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Pages (from-to) | 25-52 |

Number of pages | 28 |

Journal | Acta Mathematica Sinica, English Series |

Volume | 15 |

Issue number | 1 |

DOIs | |

State | Published - 1999 |

### Keywords

- Defect measure
- Generalized varifold
- Harmonic mapping
- Rectifiability

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics