On the limit p → ∞ of global minimizers for a p-Ginzburg-Landau-type energy

Yaniv Almog; Leonid Berlyand; Dmitry Golovaty; Itai Shafrir

doi:https://doi.org/10.1016/j.anihpc.2012.12.013

On the limit p → ∞ of global minimizers for a p-Ginzburg-Landau-type energy

Yaniv Almog, Leonid Berlyand, Dmitry Golovaty, Itai Shafrir

Mathematics

Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

We study the limit p→∞ of global minimizers for a p-Ginzburg-Landau-type energy E_p(u) = ∫ δu ^p+1/2(1-u²)² The minimization is carried over maps on ℝ² that vanish at the origin and are of degree one at infinity. We prove locally uniform convergence of the minimizers on ℝ² and obtain an explicit formula for the limit on B(0,2). Some generalizations to dimension N≥3 are presented as well.

Original language	English
Pages (from-to)	1159-1174
Number of pages	16
Journal	Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume	30
Issue number	6
DOIs	https://doi.org/10.1016/j.anihpc.2012.12.013
State	Published - 2013

All Science Journal Classification (ASJC) codes

Analysis
Mathematical Physics
Applied Mathematics

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https://doi.org/10.1016/j.anihpc.2012.12.013

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title = "On the limit p → ∞ of global minimizers for a p-Ginzburg-Landau-type energy",

abstract = "We study the limit p→∞ of global minimizers for a p-Ginzburg-Landau-type energy Ep(u) = ∫ δu p+1/2(1-u2)2 The minimization is carried over maps on ℝ2 that vanish at the origin and are of degree one at infinity. We prove locally uniform convergence of the minimizers on ℝ2 and obtain an explicit formula for the limit on B(0,2). Some generalizations to dimension N≥3 are presented as well.",

author = "Yaniv Almog and Leonid Berlyand and Dmitry Golovaty and Itai Shafrir",

note = "Funding Information: I. Shafrir was supported in part by US–Israel BSF grant no. 2010194. Y. Almog, L. Berlyand, and D. Golovaty were supported in part by NSF grants DMS-1109030, DMS-1106666, and DMS-1009849, respectively. Their travel was supported by US–Israel BSF grant no. 2010194.",

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doi = "https://doi.org/10.1016/j.anihpc.2012.12.013",

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journal = "Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire",

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T1 - On the limit p → ∞ of global minimizers for a p-Ginzburg-Landau-type energy

AU - Almog, Yaniv

AU - Berlyand, Leonid

AU - Golovaty, Dmitry

AU - Shafrir, Itai

N1 - Funding Information: I. Shafrir was supported in part by US–Israel BSF grant no. 2010194. Y. Almog, L. Berlyand, and D. Golovaty were supported in part by NSF grants DMS-1109030, DMS-1106666, and DMS-1009849, respectively. Their travel was supported by US–Israel BSF grant no. 2010194.

PY - 2013

Y1 - 2013

N2 - We study the limit p→∞ of global minimizers for a p-Ginzburg-Landau-type energy Ep(u) = ∫ δu p+1/2(1-u2)2 The minimization is carried over maps on ℝ2 that vanish at the origin and are of degree one at infinity. We prove locally uniform convergence of the minimizers on ℝ2 and obtain an explicit formula for the limit on B(0,2). Some generalizations to dimension N≥3 are presented as well.

AB - We study the limit p→∞ of global minimizers for a p-Ginzburg-Landau-type energy Ep(u) = ∫ δu p+1/2(1-u2)2 The minimization is carried over maps on ℝ2 that vanish at the origin and are of degree one at infinity. We prove locally uniform convergence of the minimizers on ℝ2 and obtain an explicit formula for the limit on B(0,2). Some generalizations to dimension N≥3 are presented as well.

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U2 - https://doi.org/10.1016/j.anihpc.2012.12.013

DO - https://doi.org/10.1016/j.anihpc.2012.12.013

M3 - مقالة

SN - 0294-1449

VL - 30

SP - 1159

EP - 1174

JO - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

JF - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

IS - 6

ER -

On the limit p → ∞ of global minimizers for a p-Ginzburg-Landau-type energy

Abstract

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