Erschienen in:

2002 | OriginalPaper | Buchkapitel

Calcul Des Variations. —Estimations d’énergie pour des applications de R3 à

verfasst von : Professor Elliott H. Lieb, Professor Michael Loss, Professor Mary Beth Ruskai

Erschienen in: Inequalities

Verlag: Springer Berlin Heidelberg

Enthalten in: Professional Book Archive

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Two problems concerning maps cp with point singularities from a domain} Ω = R3 to S2are solved. The first is to determine the minimum energy of ϕ when the location and topological degree of the singularities are prescribed. In the second problem Ω is the unit ball and ϕ = g is given on ΦΩ; we show that the only cases in which g (x/|x|) minimizes the energy is g = const, or g(x)= ±R x with R a rotation

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