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Nonlocal Equations on Domains and Manifolds Without Symmetries
Abstract
In this work, we establish existence and regularity results for solutions to nonlinear nonlocal equations of the form f(Δ)u = U(x,u) and f(Δg)u = U(x,u) in Euclidean and Riemannian settings, respectively. We prove existence results across three distinct geometric scenarios: bounded domains in ℝn, perturbed equations on compact Riemannian manifolds, and noncompact Cartan-Hadamard manifolds under suitable geometric curvature conditions.
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BibTeX
@misc{castellanos2026nonlocal,
title = {{Nonlocal Equations on Domains and Manifolds Without Symmetries}},
author = {Santiago Castellanos},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.28572},
eprint = {2610.28572},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.28572},
}
RIS
TY - UNPB
TI - Nonlocal Equations on Domains and Manifolds Without Symmetries
AU - Santiago Castellanos
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.28572
UR - https://arxiv.org/abs/2610.28572
AB - In this work, we establish existence and regularity results for solutions to nonlinear nonlocal equations of the form f(Δ)u = U(x,u) and f(Δ_g)u = U(x,u) in Euclidean and Riemannian settings, respectively. We prove existence results across three distinct geometric scenarios: bounded domains in ℝ^n, perturbed equations on compact Riemannian manifolds, and noncompact Cartan-Hadamard manifolds under suitable geometric curvature conditions.
ER -