Jerrard, Robert L. Lower bounds for generalized Ginzburg–Landau functionals. (English) Zbl 0928.35045 SIAM J. Math. Anal. 30, No. 4, 721-746 (1999). The author studies properties of Ginzburg-Landau functionals expressed by the integral of \[ | \nabla u| ^n/n+(1-| u| ^2)^2/(4\varepsilon^2), \] where \(u\in W^{1,n}(U; R^n)\), \(U\subset R^n\). Such information can be useful in the analysis of PDE’s associated with those functionals. The lower bounds relating the energy to the Brower degree of \(u\) are established, and it is proved that the energy concentrates on a small number of small sets. As a consequence, some compactness theorems are derived. Also, the results are applied to the functional which is related to the magnetic potential. Reviewer: P.B.Dubovskiĭ (Moskva) Cited in 1 ReviewCited in 89 Documents MSC: 35J50 Variational methods for elliptic systems 58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces 35Q99 Partial differential equations of mathematical physics and other areas of application Keywords:energy concentration; compactness; magnetic potential; Brower degree PDF BibTeX XML Cite \textit{R. L. Jerrard}, SIAM J. Math. Anal. 30, No. 4, 721--746 (1999; Zbl 0928.35045) Full Text: DOI OpenURL