Ginzburg-Landau minimizers with prescribed degrees: Dependence on domain

Leonid Berlyand; Petru Mironescu

doi:10.1016/S1631-073X(03)00331-5

Ginzburg-Landau minimizers with prescribed degrees: Dependence on domain

Leonid Berlyand
, Petru Mironescu

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

4 Scopus citations

Abstract

We study minimizers of the Ginzburg-Landau functional in an annular type domain with holes. We assume degrees 1 and -1 on the boundary of the annulus, degree 0 on the boundaries of the holes. Two types of qualitatively different behavior of minimizers occur, depending on the value of the H¹-capacity of the domain. We also describe the asymptotic behavior of minimizers as the coherency length tends to ∞.

Original language	English (US)
Pages (from-to)	375-380
Number of pages	6
Journal	Comptes Rendus Mathematique
Volume	337
Issue number	6
DOIs	https://doi.org/10.1016/S1631-073X(03)00331-5
State	Published - Sep 15 2003

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1016/S1631-073X(03)00331-5

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title = "Ginzburg-Landau minimizers with prescribed degrees: Dependence on domain",

abstract = "We study minimizers of the Ginzburg-Landau functional in an annular type domain with holes. We assume degrees 1 and -1 on the boundary of the annulus, degree 0 on the boundaries of the holes. Two types of qualitatively different behavior of minimizers occur, depending on the value of the H1-capacity of the domain. We also describe the asymptotic behavior of minimizers as the coherency length tends to ∞.",

author = "Leonid Berlyand and Petru Mironescu",

note = "Funding Information: The authors thank H. Brezis for useful discussions. The work of L.B. was supported by NSF grant DMS-0204637. The work of P.M. is part of the RTN Program “Fronts-Singularities”. Part of this work was done while both authors were visiting the Rutgers University. They thank the Mathematics Department for its hospitality.",

year = "2003",

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doi = "10.1016/S1631-073X(03)00331-5",

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T1 - Ginzburg-Landau minimizers with prescribed degrees

T2 - Dependence on domain

AU - Berlyand, Leonid

AU - Mironescu, Petru

N1 - Funding Information: The authors thank H. Brezis for useful discussions. The work of L.B. was supported by NSF grant DMS-0204637. The work of P.M. is part of the RTN Program “Fronts-Singularities”. Part of this work was done while both authors were visiting the Rutgers University. They thank the Mathematics Department for its hospitality.

PY - 2003/9/15

Y1 - 2003/9/15

N2 - We study minimizers of the Ginzburg-Landau functional in an annular type domain with holes. We assume degrees 1 and -1 on the boundary of the annulus, degree 0 on the boundaries of the holes. Two types of qualitatively different behavior of minimizers occur, depending on the value of the H1-capacity of the domain. We also describe the asymptotic behavior of minimizers as the coherency length tends to ∞.

AB - We study minimizers of the Ginzburg-Landau functional in an annular type domain with holes. We assume degrees 1 and -1 on the boundary of the annulus, degree 0 on the boundaries of the holes. Two types of qualitatively different behavior of minimizers occur, depending on the value of the H1-capacity of the domain. We also describe the asymptotic behavior of minimizers as the coherency length tends to ∞.

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UR - https://www.scopus.com/pages/publications/0142184318#tab=citedBy

U2 - 10.1016/S1631-073X(03)00331-5

DO - 10.1016/S1631-073X(03)00331-5

M3 - Article

AN - SCOPUS:0142184318

SN - 1631-073X

VL - 337

SP - 375

EP - 380

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

IS - 6

ER -

Ginzburg-Landau minimizers with prescribed degrees: Dependence on domain

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