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

[摘要] In this paper we establish commutator estimates for the Dirichlet-to-Neumann Map associated to a divergence form elliptic operator in the upper half-space R-+(n+1) := {(x, t) is an element of R-n x (0, infinity)}, with uniformly complex elliptic, L-infinity, 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. (C) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-12-15

[关键词] Commutator;Dirichlet-to-Neumann map;Divergence form elliptic operator;Dahlberg's bilinear estimate;Layer potentials