A system of local/nonlocal p -Laplacians: The eigenvalue problem and its asymptotic limit as p→∞

2021/04/27 by Stefano Buccheri, João Vítor da Silva, Luís H. de Miranda · 1 voice
Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Advanced Mathematical Modeling in Engineering #Spectral Theory in Mathematical Physics

paper · doi:10.3233/asy-211702

openalex created_date 2020/01/23 · openalex publication_date 2021/04/27 · openalex updated_date 2026/07/30

Abstract

In this work, given [Formula: see text], we prove the existence and simplicity of the first eigenvalue [Formula: see text] and its corresponding eigenvector [Formula: see text], for the following local/nonlocal PDE system [Formula: see text] where [Formula: see text] is a bounded open domain, [Formula: see text] and [Formula: see text]. Moreover, we address the asymptotic limit as [Formula: see text], proving the explicit geometric characterization of the corresponding first ∞-eigenvalue, namely [Formula: see text], and the uniformly convergence of the pair [Formula: see text] to the ∞-eigenvector [Formula: see text]. Finally, the triple [Formula: see text] verifies, in the viscosity sense, a limiting PDE system.

Citations

• Fractional p-eigenvalues
• Hitchhikerʼs guide to the fractional Sobolev spaces
• Recent progresses in the theory of nonlinear nonlocal problems
• Sharp regularity estimates for quasi-linear elliptic dead core problems and applications
• Regularity properties for p−dead core problems and their asymptotic limit as p→∞

Discussions

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