The Neumann condition for the superposition of fractional Laplacians

2024/02/08 by Serena Dipierro, Dipierro, Serena, Edoardo Proietti Lippi +5 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2402.05514

openalex publication_date 2024/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03

Abstract

We present a new functional setting for Neumann conditions related to the superposition of (possibly infinitely many) fractional Laplace operators. We will introduce some bespoke functional framework and present minimization properties, existence and uniqueness results, asymptotic formulas, spectral analyses, rigidity results, integration by parts formulas, superpositions of fractional perimeters, as well as a study of the associated heat equation.

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• Nontrivial solutions for nonlinear problems driven by a superposition of fractional p-Laplacians with Neumann boundary conditions

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