Radial limits of solutions to elliptic partial differential equations

2022/08/04 by P. M. Gauthier, Mohammad Mahdi A. Shirazi, Gauthier, Paul M. +1
Computer Science · Mathematics · #30D40 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Analytic and geometric function theory #Complex Variables (math.CV) #Differential Equations and Boundary Problems #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2208.02399

openalex publication_date 2022/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For certain elliptic differential operators L, we study the behaviour of solutions to Lu=0, as we tend to the boundary along radii in strictly starlike domains in \Rⁿ, n≥ 3. Analogous results are obtained in other special domains. Our approach involves introducing harmonic line bundles as instances of Brelot harmonic spaces and approximating continuous functions by harmonic functions on appropriate subsets. These approximation theorems on harmonic spaces yield interesting examples for approximation by solutions of Lu=0 on some domains in \Rⁿ.

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