摘要
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<sup>1,α</sup> 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<sup>1,α</sup> continuous away from a closed subset ∑=spt μ∪S with H<sup>n-p</sup>（S）=0.Finally,we discuss the possible varifolds type theory for Sobolev mappings.
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<sup>1,α</sup> 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<sup>1,α</sup> continuous away from a closed subset ∑=spt μ∪S with H<sup>n-p</sup>（S）=0.Finally,we discuss the possible varifolds type theory for Sobolev mappings.
基金
Partially supported by NSF Grant DMS 9626166
