TY - RPRT
T1 - Friedrichs systems in a Hilbert space framework: solvability and multiplicity
Y1 - 2017
A1 - Nenad AntoniÄ‡
A1 - Marko Erceg
A1 - Alessandro Michelangeli
AB - The Friedrichs (1958) theory of positive symmetric systems of first order partial differential equations encompasses many standard equations of mathematical physics, irrespective of their type. This theory was recast in an abstract Hilbert space setting by Ern, Guermond and Caplain (2007), and by AntoniÄ‡ and Burazin (2010). In this work we make a further step, presenting a purely operator-theoretic description of abstract Friedrichs systems, and proving that any pair of abstract Friedrichs operators admits bijective extensions with a signed boundary map. Moreover, we provide suffcient and necessary conditions for existence of infinitely many such pairs of spaces, and by the universal operator extension theory (Grubb, 1968) we get a complete identification of all such pairs, which we illustrate on two concrete one-dimensional examples.
UR - http://preprints.sissa.it/handle/1963/35280
U1 - 35587
U2 - Mathematics
U4 - 1
ER -