A Ginzburg–Landau Type Energy with Weight and with Convex Potential Near Zero

Hadiji, Rejeb; Perugia, Carmen

doi:10.3390/math8060997

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2022

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“…In [14], the authors considered the asymptotic behaviour of minimizing solutions of a Ginzburg-Landau type functional with a positive weight and with convex potential near 0 and they estimated the energy in this case. They also generalized the lower bound for the energy for the Ginzburg-Landau energy of unit vector field given initially by Brezis-Merle-Riviière in [9] for the case where the potential has a zero of infinite order.…”

Section: Introductionmentioning

confidence: 99%

A Liouville type result and quantization effects on the system $-Δu = u J'(1-|u|^{2})$ for a potential convex near zero

Maio¹,

Hadiji²,

Lefter³

et al. 2022

Preprint

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We consider a Ginzburg-Landau type equation in R 2 of the form −∆u = uJ ′ (1 − |u| 2 ) with a potential function J satisfying weak conditions allowing for example a zero of infinite order in the origin. We extend in this context the results concerning quantization of finite potential solutions of H.Brezis, F.Merle, T.Rivière from [9] who treat the case when J behaves polinomially near 0, as well as a result of Th. Cazenave, found in the same reference, and concerning the form of finite energy solutions.

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Section: Introductionmentioning

confidence: 99%