The Neumann problem of Laplace's equation in semiconvex domains. (March 2016)

• Record Type: Journal Article
• Authors: Yang, Sibei
• Is Part Of: Nonlinear analysis. Volume 133(2016)
• Page Start: 275
• Page End: 291
• Publication Date: 2016-03
• Subjects: primary 35J25 -- secondary 35J05; Neumann problem -- Semiconvex domain -- Reverse Hölder's inequality; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2015.12.017
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: Let n ≥ 2 and Ω be a bounded semiconvex domain in R n . In this paper, we show that the Neumann problem for Laplace's equation in Ω with boundary data in L p ( ∂ Ω ) is uniquely solvable for p ∈ ( 1, ∞ ), which improves the well-known result for the Neumann problem.