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The author studies the asymptotic behavior of the radial minimizer of the p -Ginzburg–Landau functional with non-vanishing Dirichlet boundary condition in the case of p ∈ ( n − 1 , n ) , where n is the dimension. The location of the zeros of the radial minimizer is discussed. Moreover the C 1 , α convergence of the radial minimizer is proved.

The author proves the uniqueness of the solution to an evolution Landau–Lifshitz type problem, when the parameter tends to zero. In addition, the unique solution is just a heat flow of a harmonic map. This uniqueness result is derived by establishing a uniform estimate for the solution.

The paper is concerned with the L loc p and the C α estimations of the gradient of u e , where u e is the minimizer of a p -energy functional. When e → 0 , the corresponding convergences of the minimizer in W 1 , p and C 1 , α senses are proved.

The author studies the asymptotic behavior of the radial minimizer of the p-Ginzburg-Landau functional with nonvanishing Dirichlet boundary condition in the case p > 2 . The location of the zeros of the radial minimizer is discussed. Moreover, the W loc 1 , p convergence of the radial minimizer is proved.

The author studies the asymptotic behavior of minimizers of a Ginzburg–Landau type functional, which is a problem being put forward by Bethuel, Brezis and Helein. The C 1 , α convergence of the regularizable minimizers is presented when the dimension n is not less than 3.