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 ...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.展开更多
Undoped p-type Ga Sb single crystals were annealed at 550–600℃ for 100 h in ambient antimony. The annealed Ga Sb samples were investigated by Hall effect measurement, glow discharge mass spectroscopy（GDMS）, infra...Undoped p-type Ga Sb single crystals were annealed at 550–600℃ for 100 h in ambient antimony. The annealed Ga Sb samples were investigated by Hall effect measurement, glow discharge mass spectroscopy（GDMS）, infrared（IR）optical transmission and photoluminescence（PL） spectroscopy. Compared with the as-grown Ga Sb single crystal, the annealed Ga Sb samples have lower hole concentrations and weak native acceptor related PL peaks, indicating the reduction of the concentration of gallium antisite related native acceptor defects. Consequently, the below gap infrared transmission of the Ga Sb samples is enhanced after the thermal treatment. The mechanism about the reduction of the native defect concentration and its influence on the material property were discussed.展开更多
This paper is devoted to investigating the asymptotic properties of the renormalized so- lution to the viscosity equation δtfε ＋ v · △↓xfε = Q（fε, fε） ＋ ε△vfε as ε →0＋. We deduce that the renorma...This paper is devoted to investigating the asymptotic properties of the renormalized so- lution to the viscosity equation δtfε ＋ v · △↓xfε = Q（fε, fε） ＋ ε△vfε as ε →0＋. We deduce that the renormalized solution of the viscosity equation approaches to the one of the Boltzmann equation in L^1（（0, T） × RN × R^N）. The proof is based on compactness analysis and velocity averaging theory.展开更多
文摘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Project supported by the National Natural Science Foundation of China(Grant Nos.61474104 and 61504131)
文摘Undoped p-type Ga Sb single crystals were annealed at 550–600℃ for 100 h in ambient antimony. The annealed Ga Sb samples were investigated by Hall effect measurement, glow discharge mass spectroscopy（GDMS）, infrared（IR）optical transmission and photoluminescence（PL） spectroscopy. Compared with the as-grown Ga Sb single crystal, the annealed Ga Sb samples have lower hole concentrations and weak native acceptor related PL peaks, indicating the reduction of the concentration of gallium antisite related native acceptor defects. Consequently, the below gap infrared transmission of the Ga Sb samples is enhanced after the thermal treatment. The mechanism about the reduction of the native defect concentration and its influence on the material property were discussed.
基金Supported by the Innovation Team Foundation of the Department of Education of Zhejiang Province (Grant No. T200924)National Natural Science Foundation of China (Grant No. 11101140)supported by National Natural Science Foundation of China (Grant No. 11071119)
文摘This paper is devoted to investigating the asymptotic properties of the renormalized so- lution to the viscosity equation δtfε ＋ v · △↓xfε = Q（fε, fε） ＋ ε△vfε as ε →0＋. We deduce that the renormalized solution of the viscosity equation approaches to the one of the Boltzmann equation in L^1（（0, T） × RN × R^N）. The proof is based on compactness analysis and velocity averaging theory.
