The ∂-Neumann problem and boundary integral equations

2021/04/19 by Bingyuan Liu, Liu, Bingyuan
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #Elasticity and Wave Propagation #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2104.09659

openalex publication_date 2021/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we find an equivalent boundary integral equation to the classical ∂-Neumann problem. The new equation contains an equivalent regularity to the global regularity of the ∂-Neumann problem. We also use the integral equations to observe a new-found rigidity property of the ∂-Neumann problem on the unit ball in ℂ².

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