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Isolated Singularities for Fractional Hartree Equations.

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Τίτλος: Isolated Singularities for Fractional Hartree Equations.
Συγγραφείς: Gu, Guangze1,2 (AUTHOR) guangzegu@163.com, Jevnikar, Aleks3 (AUTHOR) aleks.jevnikar@uniud.it, Yang, Zhipeng1,2 (AUTHOR) yangzhipeng326@163.com
Πηγή: Communications in Contemporary Mathematics. Sep2026, p1. 36p.
Θεματικοί όροι: *Mathematical singularities, *Partial differential equations, *Symmetry, *Laplacian operator
Περίληψη: In this paper, we study isolated singularities of positive solutions to a fractional Hartree equation with Riesz interaction: (−Δ)su = ∫ℝN∖{0} up(y) |x − y|μdyuqin ℝN∖{0}. The puncture changes the passage from the differential equation to its integral form: A fractional fundamental solution term may occur at the singular point. Under an upper bound at the scale of the fundamental solution and a weighted integrability condition on the source, we derive a Riesz decomposition with a nonnegative singular term. Under the same assumptions, if in addition the solution blows up at the puncture, p,q ≥ 1, and both Kelvin weights are nonnegative, an off-center moving spheres argument yields radial symmetry and strict radial decrease. We also classify positive radial homogeneous singular solutions under the corresponding convergence conditions. If a nonzero positive radial homogeneous scaling limit exists and solves the limiting equation, this classification uniquely determines its coefficient. [ABSTRACT FROM AUTHOR]
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An: 197303525
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  Data: Isolated Singularities for Fractional Hartree Equations.
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  Data: <searchLink fieldCode="AR" term="%22Gu%2C+Guangze%22">Gu, Guangze</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> guangzegu@163.com</i><br /><searchLink fieldCode="AR" term="%22Jevnikar%2C+Aleks%22">Jevnikar, Aleks</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> aleks.jevnikar@uniud.it</i><br /><searchLink fieldCode="AR" term="%22Yang%2C+Zhipeng%22">Yang, Zhipeng</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> yangzhipeng326@163.com</i>
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  Data: <searchLink fieldCode="JN" term="%22Communications+in+Contemporary+Mathematics%22">Communications in Contemporary Mathematics</searchLink>. Sep2026, p1. 36p.
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  Data: *<searchLink fieldCode="DE" term="%22Mathematical+singularities%22">Mathematical singularities</searchLink><br />*<searchLink fieldCode="DE" term="%22Partial+differential+equations%22">Partial differential equations</searchLink><br />*<searchLink fieldCode="DE" term="%22Symmetry%22">Symmetry</searchLink><br />*<searchLink fieldCode="DE" term="%22Laplacian+operator%22">Laplacian operator</searchLink>
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  Label: Abstract
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  Data: In this paper, we study isolated singularities of positive solutions to a fractional Hartree equation with Riesz interaction: (−Δ)su = ∫ℝN∖{0} up(y) |x − y|μdyuqin ℝN∖{0}. The puncture changes the passage from the differential equation to its integral form: A fractional fundamental solution term may occur at the singular point. Under an upper bound at the scale of the fundamental solution and a weighted integrability condition on the source, we derive a Riesz decomposition with a nonnegative singular term. Under the same assumptions, if in addition the solution blows up at the puncture, p,q ≥ 1, and both Kelvin weights are nonnegative, an off-center moving spheres argument yields radial symmetry and strict radial decrease. We also classify positive radial homogeneous singular solutions under the corresponding convergence conditions. If a nonzero positive radial homogeneous scaling limit exists and solves the limiting equation, this classification uniquely determines its coefficient. [ABSTRACT FROM AUTHOR]
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RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1142/s0219199726500793
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 36
        StartPage: 1
    Subjects:
      – SubjectFull: Mathematical singularities
        Type: general
      – SubjectFull: Partial differential equations
        Type: general
      – SubjectFull: Symmetry
        Type: general
      – SubjectFull: Laplacian operator
        Type: general
    Titles:
      – TitleFull: Isolated Singularities for Fractional Hartree Equations.
        Type: main
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      – PersonEntity:
          Name:
            NameFull: Gu, Guangze
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          Name:
            NameFull: Jevnikar, Aleks
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          Name:
            NameFull: Yang, Zhipeng
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          Dates:
            – D: 26
              M: 09
              Text: Sep2026
              Type: published
              Y: 2026
          Identifiers:
            – Type: issn-print
              Value: 02191997
          Titles:
            – TitleFull: Communications in Contemporary Mathematics
              Type: main
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