L² estimates for commutators of the Dirichlet-to-Neumann Map associated to elliptic operators with complex-valued bounded measurable coefficients on ℝⁿ⁺¹₊

2021/02/13 by Steve Hofmann, Guoming Zhang, Hofmann, Steve +1
Computer Science · Mathematics · #35 #42 #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2102.06835

openalex publication_date 2021/02/13 · openalex created_date 2021/03/01 · openalex updated_date 2026/07/28

Abstract

In this paper we establish commmutator estimates for the Dirichlet-to-Neumann Map associated to a divergence form elliptic operator in the upper half-space ℝⁿ⁺¹₊:=\(x,t)∈ ℝⁿ × (0,∞)\, with uniformly complex elliptic, L^∞, t-independent coefficients. By a standard pull-back mechanism, these results extend corresponding results of Kenig, Lin and Shen for the Laplacian in a Lipschitz domain, which have application to the theory of homogenization.

Citations

• Some new function spaces and their applications to Harmonic analysis
• Poisson semigroups and singular integrals

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