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

In: Inequalities

Author

Listed:
  • Elliott H. Lieb

    (Princeton University, Departments of Mathematics and Physics)

  • Michael Loss

    (Georgia Tech, School of Mathematics)

  • Mary Beth Ruskai

    (University of Massachusetts Lowell, Department of Mathematics)

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

Suggested Citation

  • Elliott H. Lieb & Michael Loss & Mary Beth Ruskai, 2002. "Calcul Des Variations. —Estimations d’énergie pour des applications de R3 à," Springer Books, in: Michael Loss & Mary Beth Ruskai (ed.), Inequalities, pages 633-636, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-55925-9_49
    DOI: 10.1007/978-3-642-55925-9_49
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