Minimizing pseudo-harmonic maps in manifolds.

Ge, Yuxin

Displaying similar documents to “Minimizing pseudo-harmonic maps in manifolds.”

On the properties of infinity-harmonic functions and an application to capacitary convex rings.

Bhattacharya, Tilak (2002)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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Remarks on the gradient of an infinity-harmonic function.

Bhattacharya, Tilak (2007)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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Example of an $\infty$ -harmonic function which is not $C^{2}$ on a dense subset.

Mikayelyan, Hayk (2005)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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Asymptotic behavior of regularizable minimizers of a Ginzburg-Landau functional in higher dimensions.

Lei, Yutian (2001)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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Asymptotics for the minimization of a Ginzburg-Landau energy in n dimensions

Paweł Strzelecki (1996)

Colloquium Mathematicae

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We prove that minimizers $u \in W^{1, n}$ of the functional $E_{} (u) = 1 / n \int_{|} {\nabla u |}^{n} d x + 1 / (4^{n}) \int_{(} 1 - {| u |}^{2})^{2} d x$ , ⊂ $ℝ^{n}$ , n ≥ 3, which satisfy the Dirichlet boundary condition $u_{} = g$ on for g: → $S^{n - 1}$ with zero topological degree, converge in $W^{1, n}$ and $C_{l o c}^{α}$ for any α<1 - upon passing to a subsequence $_{k} \to 0$ - to some minimizing n-harmonic map. This is a generalization of an earlier result obtained for n=2 by Bethuel, Brezis, and Hélein. An example of nonunique asymptotic behaviour (which cannot occur in two dimensions if deg g = 0) is presented.