L^p polyharmonic Robin problems on Lipschitz domains

2017/12/04 by Weifeng Li, Li, Weifeng, Pei Dang +7
Computer Science · Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.1712.00939

14 pages

openalex publication_date 2017/12/04 · arxiv created 2019/06/15 · arxiv updated 2019/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study a class of boundary value problems (BVPs) with Robin conditions in some L^p spaces for polyharmonic equation on Lipschitz domains. Utilizing polyharmonic fundamental solutions, these Robin BVPs are solved by the method of layer potentials. The crucial ingedients of our approach are the classical single layer potential and its higher order analog (which are called multi-layer S-potentials), and the main results generalize ones of second order (Laplacian) case to higher order (polyharmonic) case.

Citations

• Higher order Poisson Kernels and L^p polyharmonic boundary value problems in Lipschitz domains

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