Functional calculus for first order systems of Dirac type and boundary value problems. I: A priori estimates for boundary value elliptic problems via first order systems (Q2801547)

The main purpose of this work is to establish a priori estimates for some classes of boundary value problems in the upper half space. The authors are mainly interested in first order systems of Dirac type. A key feature in the present work is that the authors do not require any kind of existence or uniqueness properties of solutions. A basic tool is the reduction of second order partial differential equations to first order systems. The advantage is that for such systems a central role is the understanding of the initial value problem. At the same time, solving the partial differential equation means inverting a boundary operator in order to create the initial data for the first order system. Some of the main abstract results of this work are applied to perturbation theory for solvability.