Commutator estimates for the Dirichlet-to-Neumann map associated to parabolic equations with complex-valued and measurable coefficients on Rn+2+

In the paper we established the L2 estimates for commutators of the Dirichlet-to-Neumann map generated by a divergence form parabolic operator, defined on IIIn+2 + , with real, symmetric and t, lambda-independent coefficient matrix, or more generally, a small complex L infinity perturbation of such. The major new challenge, compared to our previous work in elliptic setting, is to handle the first order derivatives with respect to the time variable t which not only fall on solutions to parabolic equations but also on auxiliary functions.(c) 2022 Elsevier Inc. All rights reserved.