Non-local equations and optimal Sobolev inequalities on compact manifolds

2022/09/26 by Carolina Rey, Rey, Carolina, Nicolas Saintier +1 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · doi:10.48550/arxiv.2209.12357

openalex publication_date 2022/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper deals with fractional Sobolev spaces on a compact Riemannian manifold. We prove a Sobolev inequality in the critical range with an optimal constant for these fractional Sobolev spaces. We use this result to study the existence of a non-trivial solution for equations driven by a non-local integro-differential operator L_K with critical non-linearity.

Cited by

• Sharp Fractional Sobolev Embeddings on Closed Manifolds

Related

• Sharp Fractional Sobolev Embeddings on Closed Manifolds
• On Critical Kirchhoff problems driven by the fractional Laplacian
• Quantitative stability of Sobolev inequalities on compact Riemannian manifolds
• Existence results for nonlocal problems governed by the regional fractional Laplacian
• Fine bounds for best constants of fractional subcritical Sobolev embeddings and applications to nonlocal PDEs