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- W1808307592 abstract "The problem (1.1) is a generalized form of a problem introduced and completely studied by Bethuel, Brezis and Helein in [3,4]. These authors proved in particular that in a starshaped domain G and with p = 1 there exists a subsequence en, exactly d singularities a1, . . . , ad in G and a smooth harmonic map u? in G{a1, . . . , ad} such that uen → u? as en tends to 0 in C loc (G{a1, . . . , ad}) for all 0 < α < 1. Moreover, (a1, . . . , ad) minimizes a renormalized energy W . For en < e0 depending only on g and G, uen has exactly d zeroes x en 1 , . . . ,x en d . These results have been generalized to arbitrary smooth domains (see [15,10]). In [9], Comte and Mironescu estimate the rate of convergence of the zero xn i to ai if (a1, . . . , ad) is a nondegenerate critical point of W . For a general bounded smooth and positive p the problem (1.1) is studied in [1,2] by Andre and Shafrir and in [3,4]. Recall that (1.1) is an approximation of the Ginzburg–Landau model for the energy of superconductors. The weight p is modeling the problem of pinning of vortices, the physical motivations are to study a thin film with variable thickness (see [11]), or to introduce impurities in the superconductor (see [14])." @default.
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- W1808307592 title "Asymptotic behavior of minimizers of a Ginzburg-Landau equation with weight near their zeroes" @default.
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