Academic Journal
Isolated Singularities for Fractional Hartree Equations.
| Τίτλος: | Isolated Singularities for Fractional Hartree Equations. |
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| 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] |
| Βάση Δεδομένων: | Academic Search Index |
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