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On Nonlocal Equations under Symmetries
Abstract
In this work, we establishes results of existence and regularity for solutions to nonlocal equations of the form f(Δ)u = U(x,u(x)) and f(Δg)u=U(x,u(x)) in the Euclidean context and Riemannian context respectively. We extend the results of \cite{Gorka 6} for the Euclidean space ℝn under cylindrically symmetry and compact Riemannian manifolds (M,g) under action of a closed Lie subgroup G ≤ Isomg(M). Our approach combines spectral theory, complex interpolation and fixed-point methods.
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BibTeX
@misc{castellanos2026nonlocal,
title = {{On Nonlocal Equations under Symmetries}},
author = {Santiago Castellanos},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.28546},
eprint = {2610.28546},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.28546},
}
RIS
TY - UNPB
TI - On Nonlocal Equations under Symmetries
AU - Santiago Castellanos
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.28546
UR - https://arxiv.org/abs/2610.28546
AB - In this work, we establishes results of existence and regularity for solutions to nonlocal equations of the form f(Δ)u = U(x,u(x)) and f(Δ_g)u=U(x,u(x)) in the Euclidean context and Riemannian context respectively. We extend the results of \cite{Gorka 6} for the Euclidean space ℝ^n under cylindrically symmetry and compact Riemannian manifolds (M,g) under action of a closed Lie subgroup G ≤ Isom_g(M). Our approach combines spectral theory, complex interpolation and fixed-point methods.
ER -