Lower bounds for the energy of unit vector fields and applications. (English) Zbl 0908.58004

J. Funct. Anal. 152, No. 2, 379-403 (1998); erratum ibid. 171, No. 1, 233 (2000).
The author gives a lower bound for the Dirichlet energy of a unit vector field defined in a perforated domain of \(\mathbb{R}^2\) with nonzero degree on the outer boundary in terms of the total diameter of the holes. Using this, the author also gives lower bounds and compactness results for Ginzburg-Laudau functionals.


58E15 Variational problems concerning extremal problems in several variables; Yang-Mills functionals
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