The ∂-Neumann operator with the Sobolev norm of integer orders

2019/05/10 by Harrington, Phillip, Liu, Bingyuan
#Analysis of PDEs (math.AP) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1905.04238

Abstract

Let Ω⊂ℂ^m be a bounded pseudoconvex domain with smooth boundary. For each k∈ℕ, we give a sufficient condition to estimate the ∂-Neumann operator in the Sobolev space W^k(Ω). The key feature of our results is a precise formula for k in terms of the geometry of the boundary of Ω.

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