Asymptotic behavior of critical points of an energy involving a loop-well potential

Petru Mironescu; Itai Shafrir

doi:10.1080/03605302.2017.1390680

Asymptotic behavior of critical points of an energy involving a loop-well potential

Petru Mironescu, Itai Shafrir

Mathematics

Technion - Israel Institute of Technology

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

Abstract

We describe the asymptotic behavior of critical points of ʃΩ[(1/2)|∇_u|²+ W(u)/ε²] when &→0. Here, W is a Ginzburg–Landau-type potential, vanishing on a simple closed curve Γ. Unlike the case of the standard Ginzburg–Landau potential W(u) = (1 − |u|²)^2/4, studied by Bethuel, Brezis and Hélein, we do not assume any symmetry on W or Γ. To overcome the diﬃculties due to the lack of symmetry, we develop new tools which might be of independent interest.

Original language	English
Pages (from-to)	1837-1870
Number of pages	34
Journal	Communications in Partial Differential Equations
Volume	42
Issue number	12
DOIs	https://doi.org/10.1080/03605302.2017.1390680
State	Published - 2 Dec 2017

Keywords

Ginzburg–Landau energy
loop-well potential
singular perturbation

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.1080/03605302.2017.1390680

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title = "Asymptotic behavior of critical points of an energy involving a loop-well potential",

abstract = "We describe the asymptotic behavior of critical points of ʃΩ[(1/2)|∇u|2+ W(u)/ε2] when &→0. Here, W is a Ginzburg–Landau-type potential, vanishing on a simple closed curve Γ. Unlike the case of the standard Ginzburg–Landau potential W(u) = (1 − |u|2)2/4, studied by Bethuel, Brezis and H{\'e}lein, we do not assume any symmetry on W or Γ. To overcome the diﬃculties due to the lack of symmetry, we develop new tools which might be of independent interest.",

keywords = "Ginzburg–Landau energy, loop-well potential, singular perturbation",

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T1 - Asymptotic behavior of critical points of an energy involving a loop-well potential

AU - Mironescu, Petru

AU - Shafrir, Itai

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N2 - We describe the asymptotic behavior of critical points of ʃΩ[(1/2)|∇u|2+ W(u)/ε2] when &→0. Here, W is a Ginzburg–Landau-type potential, vanishing on a simple closed curve Γ. Unlike the case of the standard Ginzburg–Landau potential W(u) = (1 − |u|2)2/4, studied by Bethuel, Brezis and Hélein, we do not assume any symmetry on W or Γ. To overcome the diﬃculties due to the lack of symmetry, we develop new tools which might be of independent interest.

AB - We describe the asymptotic behavior of critical points of ʃΩ[(1/2)|∇u|2+ W(u)/ε2] when &→0. Here, W is a Ginzburg–Landau-type potential, vanishing on a simple closed curve Γ. Unlike the case of the standard Ginzburg–Landau potential W(u) = (1 − |u|2)2/4, studied by Bethuel, Brezis and Hélein, we do not assume any symmetry on W or Γ. To overcome the diﬃculties due to the lack of symmetry, we develop new tools which might be of independent interest.

KW - Ginzburg–Landau energy

KW - loop-well potential

KW - singular perturbation

UR - http://www.scopus.com/inward/record.url?scp=85032789258&partnerID=8YFLogxK

U2 - 10.1080/03605302.2017.1390680

DO - 10.1080/03605302.2017.1390680

M3 - مقالة

SN - 0360-5302

VL - 42

SP - 1837

EP - 1870

JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

IS - 12

ER -

Asymptotic behavior of critical points of an energy involving a loop-well potential

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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