ON STABILITY OF SQUARE ROOT DOMAINS FOR NON‐SELF‐ADJOINT OPERATORS UNDER ADDITIVE PERTURBATIONS
Fritz Gesztesy, Steve Hofmann, Roger Nichols · Mathematika · 2015
Assuming to be an m-accretive operator in the complex Hilbert space , we use a resolvent method due to Kato to appropriately define the additive perturbation and prove stability of square root domains, that is, Moreover, assuming in addition that , we prove stability of square root domains in the form which is most suitable for partial differential equation applications. We apply this approach to elliptic second-order partial differential operators of the form in on certain open sets , , with Dirichlet, Neumann, and mixed boundary conditions on , under general hypotheses on the (typically, non-smooth, unbounded) coefficients and on .