Commutator Estimates for the Dirichlet-to-Neumann Map in Lipschitz Domains

TL;DR

This paper derives new commutator estimates for the Dirichlet-to-Neumann map in Lipschitz domains, enhancing understanding of elliptic systems in irregular geometries.

Contribution

It introduces novel commutator estimates for the Dirichlet-to-Neumann map in Lipschitz domains using Dahlberg's bilinear estimates.

Findings

Established two new commutator estimates for elliptic systems

Applied Dahlberg's bilinear estimates to boundary value problems

Improved understanding of elliptic operators in irregular domains

Abstract

We establish two commutator estimates for the Dirichlet-to-Neumann map associated with a second-order elliptic system in divergence form in Lipschitz domains. Our approach is based on Dahlberg's bilinear estimates.