Constrained minimum Riesz energy problems for a condenser with intersecting plates

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Standard

Constrained minimum Riesz energy problems for a condenser with intersecting plates. / Dragnev, Peter D.; Fuglede, Bent; Hardin, Doug P.; Saff, Edward B.; Zorii, Natalia.

I: Journal d'Analyse Mathematique, Bind 140, Nr. 1, 2020, s. 117-159.

Publikation: Bidrag til tidsskriftTidsskriftartikelfagfællebedømt

Harvard

Dragnev, PD, Fuglede, B, Hardin, DP, Saff, EB & Zorii, N 2020, 'Constrained minimum Riesz energy problems for a condenser with intersecting plates', Journal d'Analyse Mathematique, bind 140, nr. 1, s. 117-159. https://doi.org/10.1007/s11854-020-0091-x

APA

Dragnev, P. D., Fuglede, B., Hardin, D. P., Saff, E. B., & Zorii, N. (2020). Constrained minimum Riesz energy problems for a condenser with intersecting plates. Journal d'Analyse Mathematique, 140(1), 117-159. https://doi.org/10.1007/s11854-020-0091-x

Vancouver

Dragnev PD, Fuglede B, Hardin DP, Saff EB, Zorii N. Constrained minimum Riesz energy problems for a condenser with intersecting plates. Journal d'Analyse Mathematique. 2020;140(1):117-159. https://doi.org/10.1007/s11854-020-0091-x

Author

Dragnev, Peter D. ; Fuglede, Bent ; Hardin, Doug P. ; Saff, Edward B. ; Zorii, Natalia. / Constrained minimum Riesz energy problems for a condenser with intersecting plates. I: Journal d'Analyse Mathematique. 2020 ; Bind 140, Nr. 1. s. 117-159.

Bibtex

@article{f7195eb0a33546feaddcd3c79c693195,
title = "Constrained minimum Riesz energy problems for a condenser with intersecting plates",
abstract = "We study the constrained minimum energy problem with an external field relative to the α-Riesz kernel x−yα−n of order α ∈ (0, n) for a generalized condenser A = (Ai)i∈I in ℝn, n ⩾ 3, whose oppositely charged plates intersect each other over a set of zero capacity. Conditions sufficient for the existence of minimizers are found, and their uniqueness and vague compactness are studied. Conditions obtained are shown to be sharp. We also analyze continuity of the minimizers in the vague and strong topologies when the condenser and the constraint both vary, describe the weighted equilibrium vector potentials, and single out their characteristic properties. Our arguments are based particularly on the simultaneous use of the vague topology and a suitable semimetric structure on a set of vector measures associated with A, and the establishment of completeness theorems for proper semimetric spaces. The results remain valid for the logarithmic kernel on ℝ2 and A with compact Ai, i ∈ I. The study is illustrated by several examples.",
author = "Dragnev, {Peter D.} and Bent Fuglede and Hardin, {Doug P.} and Saff, {Edward B.} and Natalia Zorii",
year = "2020",
doi = "10.1007/s11854-020-0091-x",
language = "English",
volume = "140",
pages = "117--159",
journal = "Journal d'Analyse Mathematique",
issn = "0021-7670",
publisher = "Magnes Press",
number = "1",

}

RIS

TY - JOUR

T1 - Constrained minimum Riesz energy problems for a condenser with intersecting plates

AU - Dragnev, Peter D.

AU - Fuglede, Bent

AU - Hardin, Doug P.

AU - Saff, Edward B.

AU - Zorii, Natalia

PY - 2020

Y1 - 2020

N2 - We study the constrained minimum energy problem with an external field relative to the α-Riesz kernel x−yα−n of order α ∈ (0, n) for a generalized condenser A = (Ai)i∈I in ℝn, n ⩾ 3, whose oppositely charged plates intersect each other over a set of zero capacity. Conditions sufficient for the existence of minimizers are found, and their uniqueness and vague compactness are studied. Conditions obtained are shown to be sharp. We also analyze continuity of the minimizers in the vague and strong topologies when the condenser and the constraint both vary, describe the weighted equilibrium vector potentials, and single out their characteristic properties. Our arguments are based particularly on the simultaneous use of the vague topology and a suitable semimetric structure on a set of vector measures associated with A, and the establishment of completeness theorems for proper semimetric spaces. The results remain valid for the logarithmic kernel on ℝ2 and A with compact Ai, i ∈ I. The study is illustrated by several examples.

AB - We study the constrained minimum energy problem with an external field relative to the α-Riesz kernel x−yα−n of order α ∈ (0, n) for a generalized condenser A = (Ai)i∈I in ℝn, n ⩾ 3, whose oppositely charged plates intersect each other over a set of zero capacity. Conditions sufficient for the existence of minimizers are found, and their uniqueness and vague compactness are studied. Conditions obtained are shown to be sharp. We also analyze continuity of the minimizers in the vague and strong topologies when the condenser and the constraint both vary, describe the weighted equilibrium vector potentials, and single out their characteristic properties. Our arguments are based particularly on the simultaneous use of the vague topology and a suitable semimetric structure on a set of vector measures associated with A, and the establishment of completeness theorems for proper semimetric spaces. The results remain valid for the logarithmic kernel on ℝ2 and A with compact Ai, i ∈ I. The study is illustrated by several examples.

UR - http://www.scopus.com/inward/record.url?scp=85084081188&partnerID=8YFLogxK

U2 - 10.1007/s11854-020-0091-x

DO - 10.1007/s11854-020-0091-x

M3 - Journal article

AN - SCOPUS:85084081188

VL - 140

SP - 117

EP - 159

JO - Journal d'Analyse Mathematique

JF - Journal d'Analyse Mathematique

SN - 0021-7670

IS - 1

ER -

ID: 242417172