Abstract
Two problems concerning maps cp with point singularities from a domain} Ω = R3 to S2 are 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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Références Bibliographiques
L. V. Kantorovich, Dokl. Akad. Nauk S.S.S.R., 37, n° 7-8, 1942, p. 227–229.
S. T. Rachev, Theory of Probability and its Appl., 29, 1985, p. 647–676.
H. Minc, Permanents, Encyclopedia of Math, and Appl, 6, Addison-Wesley, Reading, Mass, 1978.
R. Schoen et K. Uhlenbeck, J. Diff. Geom., 17, 1982, p. 307–335 et 18, 1983, p. 253-268.
L. SIMON, Annals of Math., 118, 1983, p. 525–571.
P. G. DE Gennes, The physics of liquid crystals, Clarendon Press, Oxford, 1974.
M. Kleman, Points, lignes, parois, Les Éditions de Physique, Orsay, 1977.
J. Ericksen, in Advances in liquid crystals, 2, G. BROWN éd., Acad. Press, New York, 1976.
H. Brezis, J.-M. CORON et F. LIEB, Harmonic maps with defects (à paraître).
W. Brinkman et P. CLADIS, Physics Today, 35, 1982, p. 48–54.
R. Hardt, D. Kinderlehrer et F. H. Lin, en préparation.
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Lieb, E.H., Loss, M., Ruskai, M.B. (2002). Calcul Des Variations. —Estimations d’énergie pour des applications de R3 à. In: Loss, M., Ruskai, M.B. (eds) Inequalities. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55925-9_49
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DOI: https://doi.org/10.1007/978-3-642-55925-9_49
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