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arXiv · 2610.28572

Nonlocal Equations on Domains and Manifolds Without Symmetries

Santiago Castellanos
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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 $f(Δ_{g})u = U(x,u)$ in Euclidean and Riemannian settings, respectively. We prove existence results across three distinct geometric scenarios: bounded domains in $\mathbb{R}^n$, perturbed equations on compact Riemannian manifolds, and noncompact Cartan-Hadamard manifolds under suitable geometric curvature conditions.

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Santiago Castellanos. 2026-10-21. Nonlocal Equations on Domains and Manifolds Without Symmetries. https://arxiv.org/abs/2610.28572

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