The Neumann problem of Laplace’s equation in semiconvex domains

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