Continuity of critical points for 1-dimensional non-local energies

In this paper we deal with the bounded critical points of a Riesz energy of attractive-repulsive type in dimension 1. Under suitable assumptions on the growth of the kernel in the origin, we are able to prove that they are continuous inside their support.

Publication Details

Journal
ArXiv.org
Published
2025-07-30
Primary Topic
Nonlinear Partial Differential Equations
Type
article
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article

Continuity of critical points for 1-dimensional non-local energies

ArXiv.org
Nonlinear Partial Differential Equations
article

Continuity of critical points for 1-dimensional non-local energies

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Abstract

In this paper we deal with the bounded critical points of a Riesz energy of attractive-repulsive type in dimension 1. Under suitable assumptions on the growth of the kernel in the origin, we are able to prove that they are continuous inside their support.

ArXiv.org
Affordable and clean energy
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Nonlinear Partial Differential Equations
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Continuity of critical points for 1-dimensional non-local energies · ArXiv.org (2025) | TGRS Research Map | TGRS