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Action-minimizing periodic orbits of the Lorentz force equation with dominant vector potential.

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Τίτλος: Action-minimizing periodic orbits of the Lorentz force equation with dominant vector potential.
Συγγραφείς: Garzón, Manuel1 (AUTHOR) mgarzon2@us.es, López-Martínez, Salvador2 (AUTHOR) salvador.lopez@uam.es
Πηγή: Calculus of Variations & Partial Differential Equations. Jun2026, Vol. 65 Issue 6, p1-20. 20p.
Θεματικοί όροι: *Lorentz force, *Calculus of variations, *Relativistic mechanics, *Limit cycles, *Electromagnetic fields, *Mathematical sequences, *Electric potential
Περίληψη: We establish the existence of non-constant periodic solutions to the Lorentz force equation, where no scalar potential is needed to induce the electromagnetic field. Our results extend to cases where a possibly singular scalar potential is present, although the vector potential assumes a leading role. The approach is based on minimizing the action functional associated with the relativistic Lagrangian. The compactness of the minimizing sequences requires the existence of negative values for the functional, which is proven using novel ideas that exploit the sign-indefinite nature of the term involving the vector potential. [ABSTRACT FROM AUTHOR]
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  – Url: https://dx.doi.org/doi:10.1007/s00526-026-03350-0
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  – Url: https://resolver.ebsco.com/c/fiv2js/result?sid=EBSCO:asx&genre=article&issn=09442669&ISBN=&volume=65&issue=6&date=20260601&spage=1&pages=1-20&title=Calculus of Variations & Partial Differential Equations&atitle=Action-minimizing%20periodic%20orbits%20of%20the%20Lorentz%20force%20equation%20with%20dominant%20vector%20potential.&aulast=Garz%C3%B3n%2C%20Manuel&id=DOI:10.1007/s00526-026-03350-0
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  Data: Action-minimizing periodic orbits of the Lorentz force equation with dominant vector potential.
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  Data: <searchLink fieldCode="AR" term="%22Garzón%2C+Manuel%22">Garzón, Manuel</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> mgarzon2@us.es</i><br /><searchLink fieldCode="AR" term="%22López-Martínez%2C+Salvador%22">López-Martínez, Salvador</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> salvador.lopez@uam.es</i>
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  Data: <searchLink fieldCode="JN" term="%22Calculus+of+Variations+%26+Partial+Differential+Equations%22">Calculus of Variations & Partial Differential Equations</searchLink>. Jun2026, Vol. 65 Issue 6, p1-20. 20p.
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  Data: *<searchLink fieldCode="DE" term="%22Lorentz+force%22">Lorentz force</searchLink><br />*<searchLink fieldCode="DE" term="%22Calculus+of+variations%22">Calculus of variations</searchLink><br />*<searchLink fieldCode="DE" term="%22Relativistic+mechanics%22">Relativistic mechanics</searchLink><br />*<searchLink fieldCode="DE" term="%22Limit+cycles%22">Limit cycles</searchLink><br />*<searchLink fieldCode="DE" term="%22Electromagnetic+fields%22">Electromagnetic fields</searchLink><br />*<searchLink fieldCode="DE" term="%22Mathematical+sequences%22">Mathematical sequences</searchLink><br />*<searchLink fieldCode="DE" term="%22Electric+potential%22">Electric potential</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: We establish the existence of non-constant periodic solutions to the Lorentz force equation, where no scalar potential is needed to induce the electromagnetic field. Our results extend to cases where a possibly singular scalar potential is present, although the vector potential assumes a leading role. The approach is based on minimizing the action functional associated with the relativistic Lagrangian. The compactness of the minimizing sequences requires the existence of negative values for the functional, which is proven using novel ideas that exploit the sign-indefinite nature of the term involving the vector potential. [ABSTRACT FROM AUTHOR]
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RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1007/s00526-026-03350-0
    Languages:
      – Code: eng
        Text: English
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      Pagination:
        PageCount: 20
        StartPage: 1
    Subjects:
      – SubjectFull: Lorentz force
        Type: general
      – SubjectFull: Calculus of variations
        Type: general
      – SubjectFull: Relativistic mechanics
        Type: general
      – SubjectFull: Limit cycles
        Type: general
      – SubjectFull: Electromagnetic fields
        Type: general
      – SubjectFull: Mathematical sequences
        Type: general
      – SubjectFull: Electric potential
        Type: general
    Titles:
      – TitleFull: Action-minimizing periodic orbits of the Lorentz force equation with dominant vector potential.
        Type: main
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          Name:
            NameFull: Garzón, Manuel
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          Name:
            NameFull: López-Martínez, Salvador
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          Dates:
            – D: 01
              M: 06
              Text: Jun2026
              Type: published
              Y: 2026
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              Value: 65
            – Type: issue
              Value: 6
          Titles:
            – TitleFull: Calculus of Variations & Partial Differential Equations
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