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Zbl 1130.49002
Millot, Vincent
The relaxed energy for $S^2$-valued maps and measurable weights. (English)
[J] Ann. Inst. Henri Poincaré, Anal. Non Linéaire 23, No. 2, 135-157 (2006). ISSN 0294-1449

Summary: We compute explicitly a relaxed type energy for maps $u: \Omega \subset \mathbb R^3 \to S^2$. The explicit formula involves the length of a minimal connection relative to some specific distance connecting the topological singularities of $u$ and associated to a measurable weight function. This result generalizes a previous result of F. Bethuel, H. Brezis and J. M. Coron.

MSC 2000:: *49J10 Free problems in several independent variables (existence)
49Q20 Variational problems in geometric measure-theoretic setting

Keywords: dipole removing technique; lower bound of energy

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