Boundary operator from matrix field formulation of boundary conditions for Friedrichs systems

Abstract

Following the recent progress in understanding the abstract setting for Friedrichs symmetric positive systems by Ern, Guermond and Caplain (2007) [8], as well as Antonić and Burazin (2010) [3], an attempt is made to relate these results to the classical Friedrichs theory. A comparison of two approaches, via the trace operator and the boundary operator, has been made, favouring the latter. Finally, a particular set of sufficient conditions for a boundary matrix field to define a boundary operator in that case is given, and the applicability of this procedure in realistic situations is shown by examples.